Question

A random sample of n = 100 observations is drawn from a population with mean equal to 21 and standard deviation equal to 20, i.e. population mean is 21 and population standard deviation is 20. Complete parts a through d below.

a. What is the probability distribution of ?̅? i.e., Give the mean and standard deviation of the sampling distribution of ?̅ and state whether it is normally distributed or not.

b. Find P ( 18.7 < ?̅ < 23.3 )

c. If standard deviation of population distribution is decreased to 10, would answer in b decrease or increase or not change? Why? (Hint: you don’t necessarily calculate the probability of P ( 18.7 < ?̅ < 23.3 ) to find the answer. Think about how the sampling distribution of ?̅ would change.)

d. If sample size increases to 200, would answer in b decrease or increase or not change? Why? (Hint: you don’t necessarily calculate the probability of P ( 18.7 < ?̅ < 23.3 ) to find the answer. Think about how the sampling distribution of ?̅ would change.)

Answer 1

Mean od the sampling distribution is 21

Standard deviation of the sampling distribution is

c. If standard deviation decreases then the probability will increase

d. If we increase the sample size to 200 then standard deviation of the sampling distribution will decrease and hence the probability increases