I need help with #2 based on the information on #1 and #1a.

If there are any missing information, I would appreciate which information is needed to solve the problem.

Thank you!

1. We will investigate the height, measured in inches, of basketball players in the dataset (variable height); call this variable X. Assume the population values of height are Normally distributed with mean 79 and standard deviation 2.5. a) (2 points) Find the probability a basketball player, selected at random, is shorter than 82 inches. Show your work. The correct probability statement is required to get full credit. Write your nal answer to 4 decimal places. 2. Please refer to the information provided in Question 1. a) (3 points) If we used samples of size n = 81 from the population, we would expect the means of those samples to follow a certain known distribution. Write the name of this known distribution and the symbols and values of the mean and standard deviation. Hint: What kind of distribution have we been using in this lab? Fill in the blanks below. Name of the Distribution: Normal Distribution Symbol and value for the mean of the sampling distribution of sample means Symbol = 1' Value = 79 Symbol and value (rounded to 4 decimal places) for the standard deviation of the sampling distribution of sample means Symbol = 3 Value = Based on the above, complete the notation below, which denotes the sampling distribution of sample means. N(_i_, 5) b) (2 points) What is the probability that the mean height of a sample of 81 basketball players is greater than 80.5 inches? Show your work. The correct probability statement is required to get full credit