Show transcribed image text Question 3: (15 points) Your friend has written a computer program that supposedly produces a sequence of in- dependent random numbers that are uniformly distributed between 0 and 1. To test this program, you ask it to generate n 1000 random samples, and compute their average a) Suppose that you find that the average of the n = 1000 samples is 0.55. Using the central limit theorem, if the generated numbers truly had a uniform distribution, what is the approzimate probability of their average being greater than or equal to 0.55? Do you believe that your friend's random number generator is correct? b) Suppose that you find that the average of the n = 1000 samples is 0.50, exactly equal to Does this give you confidence that your the true mean of the target uniform distri friend's random number generator is correct? Why or why not? bution.

Question 3: (15 points) Your friend has written a computer program that supposedly produces a sequence of in- dependent random numbers that are uniformly distributed between 0 and 1. To test this program, you ask it to generate n 1000 random samples, and compute their average a) Suppose that you find that the average of the n = 1000 samples is 0.55. Using the central limit theorem, if the generated numbers truly had a uniform distribution, what is the approzimate probability of their average being greater than or equal to 0.55? Do you believe that your friend's random number generator is correct? b) Suppose that you find that the average of the n = 1000 samples is 0.50, exactly equal to Does this give you confidence that your the true mean of the target uniform distri friend's random number generator is correct? Why or why not? bution.