Suppose that battery life is a normal random variable with μ = 8 and σ = 1.2. using the standard deviation rule, what is the probability that a randomly chosen battery will last between 6.8 and 9.2 hours?
The probability that a randomly chosen battery will last between 6.8 as well as 9.2 hrs will be "0.68".
According to the question,
μ = 8 σ = 1.2The probability that data values lies within standard deviation i.e.,
→ [tex](\mu -6) (\mu +6)[/tex] will be [tex]0.68[/tex]
The probability that data values lies within two standard deviation i.e.,
→ [tex](\mu -26)(\mu +26)[/tex] will be [tex]0.95[/tex]
The probability that data values lies within three standard deviation i.e.,
→ [tex](\mu -36) (\mu +36)[/tex] will be [tex]0.997[/tex]
Throughout the above examples,
→ [tex]\mu-6 = 8-1.2[/tex]
[tex]= 6.8[/tex]
→ [tex]\mu +6 = 8+ 1.2[/tex]
[tex]= 9.2[/tex]
Thus the above answer is correct.
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The probability that a randomly chosen battery will last between 6.8 and 9.2 hours, given a normal distribution with a mean of 8 hours and a standard deviation of 1.2 hours, is approximately 68.2% according to the empirical rule.
Calculating the Probability Using the Standard Deviation Rule
To calculate the probability of a battery lasting within this range, we find the z-scores for both limits and look up the corresponding areas under the normal distribution curve.
The standard deviation rule (or the 68-95-99.7 rule) tells us that for a normally distributed variable with mean (μ) and standard deviation (σ), approximately:
68% of the data falls within 1 standard deviation of the mean (μ ± σ).
95% of the data falls within 2 standard deviations of the mean (μ ± 2σ).
99.7% of the data falls within 3 standard deviations of the mean (μ ± 3σ).
Z-scores:
For 6.8 hours: (6.8 - μ) / σ =α- 1 hours)
For 6.8 hours: (6.8 - 8) / 1.2 = -1
For 9.2 hours: (9.2 - 8) / 1.2 = 1
The z-score corresponds to the number of standard deviations a value is from the mean. A z-score of -1 or 1 for a normal distribution typically encapsulates around 68.2% of the data (as part of the empirical rule).
Thus, we can say that the probability of a battery lasting between 6.8 and 9.2 hours is approximately 68.2%.
From beginning to end, explain the steps required to make a peanut butter and jelly sandwich.
Answer:
take 2 peices of bread
apply jelly
apply penut butter
Put the two peices of bread together
Step-by-step explanation:
edmentem
a 60 foot tree casts a shadow 85ft long. the sine of the angle between the ground and the line that connects the tip of the shadow to the top of the tree is approximately?
The sine of the angle between the ground and the line that connects the tip of the shadow to the top of the tree is approximately 0.7059.
Explanation:To find the sine of the angle between the ground and the line that connects the tip of the shadow to the top of the tree, we can use the properties of similar triangles. Let's label the height of the tree as 'a' and the length of the shadow as 'b'. We have a right triangle with the height as the opposite side and the shadow as the adjacent side. The sine of the angle can be found using the formula sine(angle) = opposite/hypotenuse, which in this case is a/b. So, the sine of the angle is a/b = 60/85 = 0.7059 (rounded to four decimal places).
Joseph needs to find the quotient of 3.216 ÷8. In what place is the first digit in the quotient?
A farmer wants to fence a rectangular area by using the wall of a barn as one side of the rectangle and then enclosing the other three sides with 160 feet of fence. find the dimensions of the rectangle that give the maximum area inside.
Final answer:
To maximize the area with 160 feet of fencing and one side provided by a barn, the fencing should create a rectangle with equal width for the two sides perpendicular to the barn. By expressing length in terms of width and using calculus to find the maximum area, we find a width of 40 feet and a length of 80 feet maximizes the area.
Explanation:
The farmer is using the barn wall as one side of the rectangular area he wants to fence. The remaining three sides require 160 feet of fencing. To maximize the area of the rectangle with a given perimeter, the shape should be a square; however, since one side is already provided by the barn, the best we can achieve is to have the two sides perpendicular to the barn be equal in length.
Let's use width w to denote the length of the two sides that are perpendicular to the barn and length l to denote the side parallel to the barn but not including the barn's wall itself. The total amount of fencing the farmer has is 160 feet, which we can express using the equation:
2w + l = 160
Since we're optimizing for area A, and A = w x l, we want to find the values of w and l that give us the maximum A. We can express l in terms of w using the perimeter equation:
l = 160 - 2w
Substituting this into the area equation gives us:
A = w x (160 - 2w) = 160w - 2w²
To find the maximum area, we take the derivative of A with respect to w and set it to zero to find critical points.
dA/dw = 160 - 4w = 0
Solving for w gives us w = 40 feet. Therefore, the dimensions that give the maximum area when one side of a rectangle is fixed are a width of 40 feet and a length of 80 feet.
For sample sizes greater than 40, the results of hypothesis tests and confidence intervals using the t distribution are highly sensitive to non-normality of the population from which samples are taken
b.the use of the t distribution assumes that the population from which the sample is drawn is normally distributed
c.for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers
d.since the t distribution procedure is robust, it can be used even for small sample with strong skewness and extreme outliers
[tex]\boxed{{\text{Option b}}}[/tex] is correct as the the use of the t distribution assumes that the population from which the sample is drawn is normally distributed.
[tex]\boxed{{\text{Option c}}}[/tex] for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers.
Further Explanation:
For sample sizes greater than [tex]40[/tex].
a) the results of hypothesis tests and confidence intervals using the t distribution are highly sensitive to non-normality of the population from which samples are taken is not correct as the sample size is large the data is normally distributed.
b) the use of the t distribution assumes that the population from which the sample is drawn is normally distributed is correct as the condition to apply t-distribution is that the data is normally distributed.
c) for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers is correct as the sample size is small the data set is less normally distributed.
d) since the t distribution procedure is robust, it can be used even for small sample with strong skewness and extreme outliers is not correct as it is the contradiction of option (c).
[tex]\boxed{{\text{Option b}}}[/tex] is correct as the the use of the t distribution assumes that the population from which the sample is drawn is normally distributed.
[tex]\boxed{{\text{Option c}}}[/tex] for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers.
Learn more:
1. Learn more about normal distribution https://brainly.com/question/12698949
2. Learn more about standard normal distribution https://brainly.com/question/13006989
Answer details:
Grade: College
Subject: Statistics
Chapter: Normal distribution
Keywords: Z-score, Z-value, standard normal distribution, standard deviation, criminologist, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion.
Evaluate. 58−(14)2=58-142= ________
The correct answer is (-138).
Sure, let's break down the calculation step by step:
1. Follow the Order of Operations (PEMDAS/BODMAS):
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)
2. Calculate Exponents:
[tex]\(14^2 = 14 \times 14 = 196\)[/tex]
3. Substitute the Exponent Result Back into the Equation:
(58 - 196 = -138)
So, [tex]\(58 - (14)^2 = -138\).[/tex]
The expression you provided is [tex]\(58 - (14)^2\).[/tex] According to the order of operations (PEMDAS/BODMAS), you first need to perform the operation inside the parentheses, which is squaring 14.
[tex]\[14^2 = 14 \times 14 = 196\][/tex]
After finding that \(14^2 = 196\), you substitute this value back into the original expression:
[58 - 196]
Finally, subtract 196 from 58:
[58 - 196 = -138]
Therefore, the correct answer is (-138).
Complete question
Evaluate. 58−(14)2=58-142= ________
Which set of ordered pairs contains only points that are on the graph of the function y = 12 − 3x?
You are building a rectangular garden and would like the area to be 32 square feet and the length twice the size as the width. What should the dimensions of your garden be?
When Kaitlin divided a fraction by 1/2, the result was a mixed number. Was the original fraction less than or greater than 1/2? Explain your reasoning
Karen works for $10 an hour. A total of 25% of her salary is deducted for taxes and insurance. She is trying to save $450 for a new set of tires. Write an equation to help determine how many hours she must work to take home $450 if she saves all of her earnings.
12+22x=-46x I don't know the answer
The answer is
x = −3/17
what is 260% as a fraction in simplest form
A cylinder and a cone each have a radius of 3 cm. and a height of 8 cm. What is the ratio of the volume of the cone to the volume of the cylinder?
I need help with all of them
Which best describes the formula for the perimeter of a rectangle? A. It’s twice the length plus the width. B. P = 2l + 2w is the perimeter of a shape. C. Double the length and width to get the perimeter. D. The formula for the perimeter of a rectangle is P = 2l + 2w.
What is the result of factoring out the GCF from the expression (24 + 36)?
A)12 × (12 + 18)
B)12 × (2 + 3)
C)6 × (8 + 12)
D)12 × (4 + 6)
Answer:
Option B is correct .i.e., 12 × ( 2 + 3 )
Step-by-step explanation:
we are Given an Expression = 24 + 36
we have to find an Expresion after factoring out GCF
Full form of GCF is Greatest Common Factor.
First we find factors of 24 and 36 then their GCF
factors of 24 - 1, 2, 3, 4, 6, 8, 12, 24
factors of 36 - 1, 2, 3, 4, 6, 9, 12, 13, 36
⇒ GCF = 12
W have,
24 + 36
⇒ 12 × 2 + 12 × 3
⇒ 12 × ( 2 + 3 )
Therefore, Option B is correct .i.e., 12 × ( 2 + 3 )
8/10 divided by 1/3 Help Needed
Gerard bought 9 hamburgers and 3 orders of fries for 24.75. Chris bought 6 hamburgers and 4 orders of fries for 19.50. Each hamburger cost the same amount. Each Order of fries cost the same amount. Wrote a system of equations that can be used to find how much one hamburger and one Order of fries cost.
A parking garage holds 300 cars on each level. There are 4 levels in the garage. How many cars can the parking garage hold in all?
The temperature in mariah’s town was at 5.2 f midnight. the temperature decreased at a steady rate of 1.1 per hour until 7:00 a.m. at 7:00 a.m. the temperature increased by a total of 4.9until noon. what was the temperature at noon?
The temperature at noon was 2.4 degrees Fahrenheit.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
To determine the temperature at noon, we need to first calculate the temperature decrease between midnight and 7:00 a.m. and then add the temperature increase from 7:00 a.m. to noon.
The temperature decreased at a rate of 1.1 degrees Fahrenheit per hour, and it took 7 hours from midnight to 7:00 a.m., so the temperature decreased by a total of 7 hours x 1.1 degrees per hour = 7.7 degrees.
The temperature at 7:00 a.m. would therefore be 5.2 degrees - 7.7 degrees = -2.5 degrees Fahrenheit.
At noon, the temperature increased by a total of 4.9 degrees, so the temperature at noon would be -2.5 degrees + 4.9 degrees = 2.4 degrees Fahrenheit.
Thus, the temperature at noon was 2.4 degrees Fahrenheit.
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A boat is traveling at a velocity represented by : 2x^3-10x^2+72x3−10x2+7. At the same time, current is pushing the boat in the same direction with a velocity given by : 5x^3+19x^2+4x5x3+19x2+4x. What is the total traveling velocity of the boat?
7x^3 +9x^2 +4x +7
Step-by-step explanation:The total velocity is represented by the sum of the two polynomials:
(2x^3-10x^2+7) + (5x^3+19x^2+4x) = x^3·(2+5) +x^2·(-10+19) +4x +7
... = 7x^3 +9x^2 +4x +7
simplify (9/4)^-3/2 x (125/27)^-2/3 x (3/5)^-2
Ray should consume 2,000 calories every day. He consumes 1,735 calories to get essential nutrients. What is Ray's discretionary calorie allowance? 115 calories 265 calories 1,735 calories 2,000 calories
Answer: 265 calories
Step-by-step explanation:
The discretionary calorie allowance is the balance of a person can take after achieving the number of calories need to get essential nutrients.
Given : Every day Energy allowance for Ray = 2,000 calories
Energy level required to get essential nutrients =1,735 calories
Then Ray's discretionary calorie allowance =
Energy allowance - Calories required to get essential nutrients
=2000-1735=265 calories
Hence, Ray's discretionary calorie allowance will be 265 calories.
14x^2-8x+3 + -6x^2+7x-11
You are ordering a hamburger and can get up to 77 toppings, but each topping can only be used once. you tell the cashier to surprise you with the toppings you get. what is the probability that you get 00 toppings? express your answer as a fraction or a decimal number rounded to four decimal places.
Find an equation of a parabola that has curvature 8 at the origin.
The curvature of a parabola y = ax^2 at the origin is given by 2a. If the curvature is 8 at the origin, a = 8/2 = 4. Therefore, the equation of a parabola that has a curvature of 8 at the origin is y = 4x^2.
Explanation:The question involves finding an equation of a parabola that has a given curvature at a specific point, the origin, in this case. This falls into the field of calculus. The curvature, also known as concavity, of a parabola y = ax^2 at the origin is given by 2a. Therefore, if the curvature is 8 at the origin, a = curvature/2 = 8/2 = 4. Hence, the equation of the parabola would be y = 4x^2 .
As an example, if we needed to find the curvature of this parabola at any other point, we can use the second derivative, which in this case is constant and equal to 8, meaning the curvature is the same at every point on the parabola. So our quadratic equation meets the given condition of having a curvature of 8 at the origin.
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Compare and contrast Euclidean geometry and spherical geometry. Be sure to include these points:
1. Describe the role of the Parallel Postulate in spherical geometry.
2. How are triangles different in spherical geometry as opposed to Euclidean geometry?
3. Geodesics
4. Applications of spherical geometry
Final answer:
Euclidean geometry and spherical geometry have distinct characteristics. The Parallel Postulate, triangle properties, geodesics, and applications differ between the two. Euclidean geometry relies on parallel lines, triangles with interior angles summing to 180 degrees, and straight geodesics, while spherical geometry lacks parallel lines, features triangles with angles >180 degrees, and utilizes great circles as geodesics. Spherical geometry finds applications in astronomy, navigation, Earth sciences, and cartography.
Explanation:
Euclidean Geometry vs Spherical Geometry
Euclidean geometry and spherical geometry are two different branches of geometry that have distinct characteristics and applications. Let's compare and contrast them:
1. Role of the Parallel Postulate
In Euclidean geometry: The Parallel Postulate states that given a line and a point not on that line, there is exactly one line that passes through the point and is parallel to the given line.
In spherical geometry: The Parallel Postulate is not true. In fact, there are no parallel lines in spherical geometry. On a sphere, any two lines will eventually intersect.
2. Triangles in Euclidean Geometry vs Spherical Geometry
In Euclidean geometry: Triangles have interior angles that sum up to 180 degrees. The angles of a triangle are classified as acute, obtuse, or right.
In spherical geometry: Triangles have interior angles that add up to more than 180 degrees. In fact, the sum can be greater than 540 degrees. Spherical triangles on a sphere are classified as acute-angled, right-angled, or obtuse-angled based on their angles.
3. Geodesics
In Euclidean geometry: Geodesics are straight lines and shortest paths between two points.
In spherical geometry: Geodesics are great circles or the arcs of circles on the surface of the sphere. They represent the shortest path between two points on a sphere.
4. Applications of Spherical Geometry
Spherical geometry has practical applications in various fields, including:
Astronomy: Spherical coordinates are used to locate celestial objects.
Navigation: Spherical trigonometry helps navigate across the Earth's curved surface.
Earth sciences: Spherical harmonics are used to represent the Earth's gravitational field.
Cartography: Representing the Earth's surface on a map or globe.
The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth. If a person weighs 180 pounds on the surface of the earth and the radius of the earth is 3900 miles, what will the person weigh if he or she is 325 miles above the earth's surface?
a rectangle is 9ft long and 40 in wide what is its area in square feet?