Suppose we know that the birth weight of babies is normally distributed with mean 3500g
and standard deviation 500g.
(1) What is the probability that a baby is born that weighs less than 3100g?
a. What are the parameters?
b. Construct the normal distribution density curve, then shade your seeking area.
c. Find the Z-score, and construct the standard normal distribution density curve,
then shade your seeking area.
d. Find the probability.
Answers
Answer:
a) [tex]\mu = 3500 gr, \sigma = 500g[/tex]
[tex]X \sim N(\mu =3500, \sigma =500)[/tex]
b) For this case we want to find this probability:
[tex] P(X< 3110)[/tex]
And in the firt figure attached we see the normal standard distirbution with the parameters given and the green area represent the probability that we want to find.
c) For this case the z score is defined as:
[tex] z =\frac{X-\mu}{\sigma}[/tex]
And replacing we got:
[tex] Z= \frac{3100-3500}{500}= -0.8[/tex]
And in the second figure attached we illustrate the probability desired in terms of the z score. With the shaded area representing the probability that z<-0.8
d) We can find this probability using the normal standard distribution or excel and we got:
[tex] P(X<3100) =P(Z<-0.8) = 0.212[/tex]
Step-by-step explanation:
For this problem we define the random variable of interest X defined as "the birth weigth of babies" and the distribution for this variable is normal
Part a
The parameters are given:
[tex]\mu = 3500 gr, \sigma = 500g[/tex]
[tex]X \sim N(\mu =3500, \sigma =500)[/tex]
Part b
For this case we want to find this probability:
[tex] P(X< 3110)[/tex]
And in the firt figure attached we see the normal standard distirbution with the parameters given and the green area represent the probability that we want to find.
Part c
For this case the z score is defined as:
[tex] z =\frac{X-\mu}{\sigma}[/tex]
And replacing we got:
[tex] Z= \frac{3100-3500}{500}= -0.8[/tex]
And in the second figure attached we illustrate the probability desired in terms of the z score. With the shaded area representing the probability that z<-0.8
Part d
We can find this probability using the normal standard distribution or excel and we got:
[tex] P(X<3100) =P(Z<-0.8) = 0.212[/tex]
Related Questions
The effect of drugs and alcohol on the nervous system has been the subject of considerable research recently. Suppose a research neurologist is testing the effect of a drug on response time by injecting 150 rats with a unit of dose of the drug, subjecting each to neurological stimulus, and recording its response time. The neurologist knows that the mean response time for rats not injected with the drug (the "control" mean) is 1.2 seconds. S/he wishes to test whether the mean response time for the drug-injected rats is greater than 1.2 seconds. If the sampling experiment is conducted with the sample mean equal to 1.05 second, set up the test of hypothesis for this experiment and determine if the results are significant. Suppose drug-injected rats have a mean response time of 1.1 .seconds, that is mu = 1.1 seconds.
Calculate the value of beta corresponding to the two rejection regions.
Answers
The student's question involves a statistical hypothesis test to compare the mean response times between drug-injected and control rats. The calculation of beta, representing the risk of Type II error, requires more information not provided in the question.
Explanation:The given scenario involves setting up a hypothesis test to determine if the mean response time for drug-injected rats is significantly different from the control group (rats not injected with the drug) with a known mean response time of 1.2 seconds. The null hypothesis would state that the mean response time for drug-injected rats (μ) is equal to 1.2 seconds (H0: μ = 1.2), while the alternative hypothesis would state that the mean response time is greater than 1.2 seconds (Ha: μ > 1.2).
Given that the sample mean response time for drug-injected rats is 1.05 seconds, which is actually lower than the control mean, this initially suggests that the drug does not increase the response time but rather decreases it or has no effect. However, as the question indicates a confusion with the typo in sample mean, we will proceed with testing the hypothesis based on the provided assumption that the drug-injected rats have a mean response time of 1.1 seconds.
To calculate the value of beta (the probability of a Type II error, which occurs when the null hypothesis is not rejected even though it is false), we would need to define the rejection regions for our test. The rejection region is typically defined based on the significance level (alpha) and the distribution of the test statistic under the null hypothesis. Without specifics such as the sample size, standard deviation, and significance level for defining the rejection regions, we cannot calculate beta directly.
The function f(x)=-(x-3)^2+9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?
Answers
Answer:
9.
Step-by-step explanation:
[tex]f(x) = -(x - 3)^2 + 9[/tex] is a parabola in its vertex form. For clarity, let [tex]f(x) = a (x - h)^2 + k[/tex] represent this function.
[tex]a = -1[/tex].[tex]h = 3[/tex].[tex]k = 9[/tex].Note that [tex]a[/tex], the leading coefficient, is negative. Therefore, this parabola opens downwards. The vertex of the parabola would be [tex](h,\, k)[/tex], which in this question is the point [tex](3,\, 9)[/tex]. Since the parabola opens downwards, that vertex would be a local maximum (a crest) on its graph.
Before concluding that the maximum area of this rectangle is [tex]9[/tex], make sure that [tex](3,\, 9)[/tex] is indeed on the graph of [tex]y = f(x)[/tex].
The length of a rectangle should be positive. Since [tex]x[/tex] represents the length of this rectangle, [tex]x > 0[/tex]. Also, since the perimeter should be less than [tex]12[/tex], the length of one side should be less than [tex]12 / 2 = 6[/tex]. Therefore, the domain of [tex]f[/tex] should be the open interval [tex](0,\, 6)[/tex]. (Endpoints not included.)
Indeed, [tex]x = 3[/tex] is in that interval. [tex](3,\, 9)[/tex] would be on the graph [tex]y = f(x)[/tex]. Therefore, [tex]9[/tex] is indeed the maximum area of this rectangle.
Side note: if the domain is a closed interval (i.e., endpoints included,) then consider checking the endpoints, as well.
Answer:
Step-by-step explanation:
9
If a circle has a diameter of 91 units how many units is the radius
Answers
Answer:
r =45.5 units
Step-by-step explanation:
The diameter is twice the radius, or the radius is 1/2 the diameter
r = d/2
r = 91/2
r =45.5 units
Answer: 45.5
Step-by-step explanation: 91/2 because to find the diameter you have to multiply the radius by 2 and now we need to reverse it
Mike runs for the president of the student government and is interested to know whether the proportion of the student body in favor of him is significantly more than 50 percent. A random sample of 100 students was taken. Fifty-five of them favored Mike. At a 0.05 level of significance, it can be concluded that the proportion of the students in favor of Mike:
a.is significantly greater than 50 percent because 55 percent of the sample favored him.
b.is not significantly greater than 50 percent.
c.is significantly greater than 55 percent.
d.is not significantly different from 55 percent.
Answers
Using the z-distribution, it is found that the correct option is:
b. is not significantly greater than 50 percent.
At the null hypothesis, it is tested if the proportion is not significantly greater than 50%, that is:
[tex]H_0: p \leq 0.5[/tex]
At the alternative hypothesis, it is tested if the proportion is significantly greater than 50%, that is:
[tex]H_1: p > 0.5[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are: [tex]n = 100, \overline{p} = \frac{55}{100} = 0.55, p = 0.5[/tex].
Hence:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.55 - 0.5}{\sqrt{\frac{0.5(0.5)}{100}}}[/tex]
[tex]z = 1[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, using the z-distribution with a significance level of 0.05, is of [tex]z^{\ast} = 1.645[/tex].
Since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that the proportion is greater than 50%, hence, option b is correct.
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In a right triangle, which ratio represents the sine of an angle?
a.
StartFraction opposite Over hypotenuse EndFraction
c.
StartFraction opposite Over opposite Endfraction
b.
StartFraction adjacent Over hypotenuse EndFraction
d.
StartFraction opposite Over adjacent EndFraction
Please sele
Answers
Answer:
A
Step-by-step explanation:
What is the absolute value of -7.95
Is it
A- -7.95
B- 7.95
C- not known
Answers
Answer:
7.95.
Step-by-step explanation:
Absolute value is the positive version of that number.
Riley planted 10 flowers.five of the flowers are purple.three are pink , and the rest are red.what fraction of the flowers is red?
Answers
Answer:
2/10 or simplified, 1/5
Step-by-step explanation:
5 are purple out of 10 flowers so 5/10. 3 are pink so 3/10. That leaves 2/10 left, and depending on what your teacher prefers, the simplified answer is 1/5. I hope this helps.
Which point is on the circle centered at the origin with a radius of 5 units?
Distance formula Vuxe - x0) + (V2 = 1
(2 √21)
(
23)
Answers
Answer:
its 2,21
Step-by-step explanation:
The only point that is in the circle of radius 5 is option A: (2, √21).
What is Polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.
The distance between a point (x, y) and the origin is:
d = √(x² + y²).
Of the given options, the only one that meets this condition is the one in option A. (2, √21).
If we find the distance to the origin, we get:
d = √(2² + √21²) = √(4 + 21) = 5.
So that is the correct option.
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Complete question:
Which point is on the circle centered at the origin with a radius of 5 units?
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
A. (2, StartRoot 21 EndRoot)
B. (2, StartRoot 23 EndRoot)
C. (2, 1)
D. (2, 3)
1
The slope of a vertical line is:
(a) o
(b) Undefined
R
(c) 1
(d) -1
Answers
Which lines have a y-intercept at (0,4)?
Answers
Answer:
Is there any picture ?
Step-by-step explanation:
A spherical boulder is 18 ft in diameter and weighs almost 8 tons. Find the volume. Use 3.14 for piπ.
Answers
The volume of a spherical boulder with a diameter of 18 ft can be calculated using the formula V = 4/3πr³, with 'r' being the radius of the sphere. By substituting the radius of 9 ft (half of 18 ft), we find that the volume is approximately 3053.62 cubic feet.
Explanation:To find the volume of a sphere, we use the formula: V = 4/3πr³, where 'r' is the radius of the sphere. The radius can be found from the diameter by dividing it by 2; therefore, for this boulder, the radius will be 18 ft/2 = 9 ft. Substituting 'r' into the volume equation: V = 4/3 * 3.14 * (9ft)³ = 3053.62 cubic feet. Therefore, the spherical boulder has a volume of approximately 3053.62 cubic feet.
To find the volume of a spherical boulder, we can use the formula for the volume of a sphere, which is V = (4/3)πr³. Given that the diameter of the boulder is 18 ft, we can find the radius by dividing the diameter by 2, which gives us a radius of 9 ft. Plugging this value into the formula, we get V = (4/3)π(9 ft)³. Using the value of π as 3.14, we can calculate the volume:
V = (4/3)(3.14)(9 ft)³ = (4/3)(3.14)(729 ft³) = 3053.96 ft³
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The speeds of a car and a train after they activate their emergency brakes are represented by the following tables:
Car
Time (seconds) Speed (m/s)
0 69.4
2 34.0
4 16.7
6 8.2
8 4.0
Train
Time (seconds) Speed (m/s)
0 88.9
2 50.1
4 28.1
6 15.8
8 8.5
Determine whether the data for cars is best modeled as a linear function or an exponential fuction.
Determine whether the data for train is best modeled as a linear function or an exponential function
Answers
Answer:
Car: Exponential Function
Train: Exponential Function
Step-by-step explanation:
The consecutive differences are quite far from being constant. However, the consecutive ratios are quite close to being constant, being approximately 0.49 for every increase in 2 seconds.Therefore, the speed of the car is best modeled by an exponential function. The consecutive ratios for the trains are quite close to being constant, being approximately 0.56 for every increase in 2 seconds. Therefore, the speed of the train is best modeled by an exponential function.
The data of car is exponential function.
The data of truck is exponential function.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
As, the difference between two consecutive terms is not constant.
but the ratios are quite close to being constant, approximately 0.49 for every increase in 2 seconds.
The consecutive ratios for the trains are 0.56 for every increase in 2 seconds.
Thus, the speed of the car and truck is an exponential function.
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Which opening sentence goes best with the details in the above paragraph?
A.
Recycling programs have become popular.
B.
Pollution from burning of fossil fuels causes acid rain.
C.
Canada is a land rich in mineral resources.
D.
The United States is rich in resources.
People have often acted as though these resources were unlimited. In recent years, however, the people of the United States have started to understand that they must use their resources more wisely than in the past.
Answers
Answer:
The United states is rich in resources
Step-by-step explanation:
Got it right on study island:))
Final answer:
The opening sentence that best fits the paragraph's context is 'The United States is rich in resources,' as it introduces the theme of resource consumption and sustainability within the U.S.
Explanation:
The best opening sentence that goes with the details in the paragraph provided is option D: The United States is rich in resources. This opening sentence sets the context for discussing how the people in the United States have historically acted as if their resources were unlimited. It leads into the realization that there must be a more prudent approach to using resources going forward, as indicated in the paragraph. The passage indicates a shift in understanding within the United States regarding resource consumption and the necessity for wiser use, aligning well with the recognition of resource richness and the implication of historical abundance.
Jada buys a bottle of laundry detergent that contains 6 cups of detergent . She uses 1/8
cup in each load of laundry she does.
How many loads of laundry can Jada do with her bottle of laundry detergent
Answers
Answer:
Jada can do 48 loads of laundry.
Step-by-step explanation:
There are 6 cups of detergent in the bottle. If Jada uses 1/8 cup of detergent each load you would have to find out how many 1/8 cups are in 6 cups. There are 8, 1/8 cups in 1 cup. So you would do 6 time 8, which equals 48 loads.
Answer: I literally gust took the the test and the answer is 112.
Your welcome!!
Charlie is driving to Boston. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Charlie has 49 miles to his destination after 15 minutes of driving, and he has 32.2 miles to his destination after 39 minutes of driving. How many miles will he have to his destination after 47 minutes of driving
Answers
Answer:26.6 miles
Step-by-step explanation:
Given
Charlie distance to his destination is a linear function of total driving time
suppose distance d is related to time t as
[tex]d=mt+c\quad \ldots(i)[/tex]
at [tex]d=49\ miles[/tex] after [tex]t=15\ min[/tex]
Substitute in (i)
[tex]49=m(15)+c\quad \ldots(ii)[/tex]
at [tex]d=32.2\ miles[/tex] after [tex]t=39\ min[/tex]
[tex]32.2=m(39)+c\quad \ldots(iii)[/tex]
Solving (ii) and (iii) we get
[tex]m=-0.7[/tex]
substitute in eq (ii) we get
[tex]c=59.5[/tex]
so after [tex]t=47\ min[/tex]
[tex]d=(-0.7)47+59.5[/tex]
[tex]d=59.5-32.9=26.6\ miles[/tex]
So 26.6 miles is left to travel after 47 minutes
How do you solve this?
Answers
A spinner with the colors red, blue, yellow, green, and orange is spun. What is the theoretical probability of landing on orange?
Answers
The theoretical probability of landing on orange when spinning a spinner with five colors is 1/5.
Since there are five colors on the spinner, each color has an equal chance of landing, so the theoretical probability of landing on orange is 1 out of 5, or 1/5.
The expression 3(1.5)^t models the number of bacteria in a culture as a function of the number of hours since the cultures was created.
What does 3 represent in this expression?
A. The culture was created 3 hours ago.
B. There were initially 3 bacteria in the culture.
C. The number of bacteria is multiplied by 3 each hour.
Answers
Answer:
3 would be the initial value so B
Step-by-step explanation:
Answer:
The answer is There were initially 3 bacteria in the culture.
Step-by-step explanation:
A bag contains 10 marbles: 3 are green, 5 are red, and 2 are blue. Karen chooses a marble at random, and without putting it back, choose another one at
random. What is the probability that both marbles she chooses are red? Write your answer as a fraction in simplest form
Answers
Answer:
don't bother commenting im a bot
Step-by-step explanation:
Answer:
5/18 I believe
Step-by-step explanation:
The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $3 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $35. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 717 cookies before the drawing. Lisa bought 31 cookies. What is the probability she will win the dinner for two? Write your answer as a fraction in simplest form, if one exists.
Answers
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images below to see the step by step explanation to the question above.
For each 11 mm of coloured fabric Nick uses to make his curtains, he also uses 2 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form.
Answers
Answer:
The amount of white fabric to coloured fabric as a ratio is 20:11
Step-by-step explanation:
We are given that For each 11 mm of colored fabric Nick uses to make his curtains, he also uses 2 cm of white fabric.
Length of colored fabric = 11 mm
Length of White fabric = 2 cm
1 cm = 10 mm
2 cm = 20 mm
So, length of white fabric = 20 mm
So, Ratio of the amount of white fabric to coloured fabric = [tex]\frac{20}{11}[/tex]
Hence the amount of white fabric to coloured fabric as a ratio is 20:11
What is (x^2+3x-10)/(x-2)
Answers
The simplified expression is x+5.
To simplify the expression x^2 +3x−10 /x−2, you can use polynomial long division or factorization.
Here's how to do it by factorization:
Factor the numerator
x^2 +3x−10:
x^2 +3x−10=(x+5)(x−2)
Rewrite the expression with the factored form of the numerator:
(x+5)(x−2)/ x−2
Cancel out the common factor of x−2:
(x−2) /(x+5) /x−2
The simplified expression is x+5.
So, x^2 +3x−10/ x−2 =x+5.
In 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?" Of the 1100 adults surveyed, 429 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 352 indicated that they were total abstainers. Has the proportion of adults who totally abstain from alcohol changed? Use the alphaequals0.10 level of significance.
Answers
Answer:
We conclude that the proportion of adults who totally abstain from alcohol has changed.
Step-by-step explanation:
We are given that in 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?"
Of the 1100 adults surveyed, 429 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 352 in
Let p = proportion of adults who totally abstain from alcohol.
where, p = [tex]\frac{429}{1100}[/tex] = 0.39
So, Null Hypothesis, [tex]H_0[/tex] : p = 39% {means that the proportion of adults who totally abstain from alcohol has not changed}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 39% {means that the proportion of adults who totally abstain from alcohol has changed}
The test statistics that would be used here One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of adults who totally abstain from alcohol = [tex]\frac{352}{1100}[/tex] = 0.32
n = sample of adults surveyed = 1100
So, test statistics = [tex]\frac{0.32-0.39}{\sqrt{\frac{0.32(1-0.32)}{1100} } }[/tex]
= -4.976
The value of z test statistics is -4.976.
Now, at 0.10 significance level the z table gives critical values of -1.645 and 1.645 for two-tailed test.
Since our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the proportion of adults who totally abstain from alcohol has changed.
A prisoner is trapped in a cell containing three doors. The first door leads to a tunnel that returns him to his cell after two days’ travel. The second leads to a tunnel that returns him to his cell after four days’ travel. The third door leads to freedom after one day of travel. If it is assumed that the prisoner will always select doors 1, 2, and 3 with respective probabilities 0.3, 0.5, and 0.2, what is the expected number of days until the prisoner reaches freedom?
Answers
The expected number of days until the prisoner reaches freedom is 2.8 days.
To find the expected number of days until the prisoner reaches freedom, we can use the concept of expected value. We'll multiply the number of days it takes to reach freedom through each door by the probability of choosing that door, and then sum up these values.
Let's denote:
[tex]- \( X_1 \)[/tex] as the number of days it takes to reach freedom through door 1 (returns to the cell after 2 days).
[tex]- \( X_2 \)[/tex] as the number of days it takes to reach freedom through door 2 (returns to the cell after 4 days).
[tex]- \( X_3 \)[/tex] as the number of days it takes to reach freedom through door 3 (direct freedom after 1 day).
Given the probabilities:
- Probability of choosing door 1: [tex]\( P(X_1) = 0.3 \)[/tex]
- Probability of choosing door 2: [tex]\( P(X_2) = 0.5 \)[/tex]
- Probability of choosing door 3: [tex]\( P(X_3) = 0.2 \)[/tex]
Now, we calculate the expected value:
[tex]\[ E[X] = P(X_1) \times X_1 + P(X_2) \times X_2 + P(X_3) \times X_3 \][/tex]
[tex]\[ E[X] = 0.3 \times 2 + 0.5 \times 4 + 0.2 \times 1 \][/tex]
[tex]\[ E[X] = 0.6 + 2 + 0.2 \][/tex]
[tex]\[ E[X] = 2.8 \][/tex]
So, the expected number of days until the prisoner reaches freedom is 2.8 days.
A market researcher for Eric’s Electronics wants to study TV viewing habits of residents in Chicago. The individuals in the survey are asked to keep track of their weekly TV viewing time. A random sample of 50 respondents is selected, and the average viewing time per week for the 50 individuals in the sample is 17.5 hours. The population standard deviation is known to be 5.0 hours. Assume that TV viewing is a normally distributed random variable. (7 points) Construct a 90% confidence interval estimate for the mean amount of television watched per week by individuals in Chicago. Interpret your result.
Answers
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.
Margin of error = z × σ/√n
Where
σ = population standard Deviation
n = number of samples
From the information given
1) x = 17.5
σ = 5
n = 50
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.95
The z score corresponding to the area on the z table is 1.645. Thus, confidence level of 90% is 1.645
Margin of error = 1.645 × 5/√50 = 1.16
Confidence interval = 17.5 ± 1.16
For a hypothesis test of H0 : μ = 8 vs. H0 : μ > 8, the sample mean of the data is computed to be 8.24. The population standard deviation is unknown; the sample standard deviation is computed, and its value is 0.29. These sample statistics are based on a sample size of 19. It is assumed that the underlying population is normally distributed. Which of the following would be the distribution of the test statistic in this scenario?a) The t-distribution with 8 degrees of freedomb) The standard normal distributionc) The t-distribution with 19 degrees of freedomd) The t-distribution with 18 degrees of freedom
Answers
Answer:
d) The t-distribution with 18 degrees of freedom
Step-by-step explanation:
If we have the population standard deviation, we use the standard normal distribution.
Otherwise, if we only have the standard deviation for the sample, we use the t-distribution.
The number of degrees of freedom is the sample size subtracted by 1.
In this problem:
Sample size of 19, we have the standard deviation for the sample.
So the t-distribution will be used to solve this question, with 19-1 = 18 degrees of freedom.
So the correct answer is:
d) The t-distribution with 18 degrees of freedom
In a hypothesis test where the population standard deviation is unknown and estimated by the sample standard deviation, we use the t-distribution with degrees of freedom equal to the sample size minus one. In this case, the distribution of the test statistic would follow a t-distribution with 18 degrees of freedom.
Explanation:In this particular case, the sample size is 19, and the population standard deviation is unknown and estimated by the sample standard deviation. Because of these conditions, the t-distribution would be used to determine the test statistic. Specifically, we would use the t-distribution with degrees of freedom equaling the sample size minus one, i.e., 18. Therefore, the correct answer among the options given is 'The t-distribution with 18 degrees of freedom'.
For example, suppose we have a set of samples from an unknown population, we compute the sample standard deviation and use it as an estimator of the actual unknown population standard deviation. In such cases, we use the t-distribution with (n-1) degrees of freedom, where n is our sample size. Here, it would be the t-distribution with 18 degrees of freedom because our sample size is 19.
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find the solution set x^2+2x-8=0 separate the two answers with a comma
Answers
Answer:
-4, 2
Step-by-step explanation:
The equation can be factored as ...
(x +4)(x -2) = 0
This has solutions that make the factors zero:
x = -4, x = 2
The solution set is {-4, 2}.
Write a recursive rule an explicit rule for the arithmetic sequence 15,22.5,30,37.5
Answers
Answer:
[tex]a_n = a_o +(n-1) d[/tex]
[tex] 22.5 = 15 +(2-1) d[/tex]
[tex] d = 22.5-15 =7.5[/tex]
The general expression is:
[tex] a_n = 15+ (n-1)*7.5 , n \geq 1[/tex]
Step-by-step explanation:
For this case we have the following arithmetic sequence given:
15, 22.5, 30,37.5
In order to fidn the recursive rule for this sequence we need to take in count that the general formula for an arithmetic sequence is given by:
[tex]a_n = a_o +(n-1) d[/tex]
Where [tex]a_n[/tex] is the nth term [tex]a_o[/tex] the initial value for the sequence and d the common difference. For this case we have that [tex]a_o =15[/tex]
And for the first term we have:
[tex] 15= 15 +(1-1)d[/tex]
For the second term we have this:
[tex] 22.5 = 15 +(2-1) d[/tex]
And solving for the value of d we got:
[tex] d = 22.5-15 =7.5[/tex]
And for the 3th term we have:
[tex] a_3= 15 +(3-1)*7.5 =30[/tex]
And for the 4th term
[tex]a_4 =15 +(4-1)*7.5 =37.5[/tex]
So then our expression is correct and would be given by:
[tex] a_n = 15+ (n-1)*7.5 , n \geq 1[/tex]
The rectangle has an area of 198 square millimeters. The length is 9 millimeters. What is the width of the rectangle?
Answers
Answer:
22 millimetres
Step-by-step explanation:
[tex]width \: of \: rectangle \\ = \frac{area}{length} \\ = \frac{198}{9} \\ = 22 \: millimeters \\ [/tex]
The membership of a student group is expressed by the equation y = 14x + 10, where x represents the number of years since the group was formed and y represents the number of members. How many years will it take for the group to have 290 members? If the group was formed in the year 2000, in what year would you expect the group to have 290 members?
Answers
Answer:
1: 20
2: 2020
Step-by-step explanation:
just got it man so ima go yeet
The group will have 290 members in the year 2020
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here, the equation is y = 14x + 10 and we are required to have 290 members thus, 290=14x + 10
x= 280/14
x = 20 years
Hence the number of years required to achieve 290 members is equal to 20 years.
Learn more about linear equations here:
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