And 1. if a person bought 1 share of google stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? hint: you do not want to calculate the mean to answer this one. the probability would be the same for any normal distribution.

The probability that the stock closed at less than the mean for that year is approximately 0.5, assuming a normal distribution.

1. In a normal distribution, the mean divides the distribution into two equal halves, with 50% of the data falling below the mean and 50% above it.

2. Therefore, the probability that a randomly chosen data point (in this case, the closing price of  stock) is below the mean is 0.5 or 50%.

Now, let's dive into the step-by-step calculation to illustrate this:

1. Identify the Mean and Standard Deviation: While you mentioned not to calculate the mean, it's important to understand that for a normal distribution, the mean is at the center and separates the distribution into equal probabilities on either side. However, we do need to know the standard deviation, which measures the spread of data points around the mean. Let's assume the mean closing price for stock over the past year is $X, and the standard deviation is $Y.

2. Use the Standard Normal Distribution: Since we're dealing with a normal distribution, we can use the standard normal distribution to find probabilities. This distribution has a mean of 0 and a standard deviation of 1.

3. Standardize the Data: To work with the standard normal distribution, we need to standardize the data point we're interested in. Let's denote the closing price of  stock on the chosen day as $Z. We standardize this value using the formula:

  [tex]\[ Z = \frac{{Z - X}}{{Y}} \][/tex]

  Here, ( Z ) is the standardized value.

4. Find the Probability: Once we have the standardized value ( Z ), we can look it up in a standard normal distribution table or use software/tools to find the probability that a randomly chosen value from a standard normal distribution is less than ( Z ). This probability will be the same as the probability that the stock closed at less than the mean for that year.

5. Conclusion: Based on the properties of a normal distribution, the probability that a randomly chosen data point (stock closing price) is below the mean is always 0.5 or 50%. This holds true regardless of the specific mean or standard deviation values for  stock.

complete question

And 1. if a person bought 1 share of  stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? hint: you do not want to calculate the mean to answer this one. the probability would be the same for any normal distribution.

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