Suppose Xis are independent and identical random variables w

Suppose Xi\'s are independent and identical random variables which follows an exponential distribution with mean 50 and standard deviation of 50, where i=1,2,3,...,100

a. What is the distribution of x bar and explain how you got the answer.

b. Find 88% confidence interval for population mean

c. What sample size needed in order to estimate the mean within plus or minus 5 with 12% type 1 error?

Solution

The mean of any distribution follow normal as sample size exceeds 30

Hence x bar has mean of 50 and std dev =50/rtn = 5

b)88% confi interval

z value =1.56

Margin of error = 1.56(5) = 7.80

Confidence interval = (50-7.8, 50+7.8)

= (42.2, 57.8)

c) Alpha =0.12

Hence z = 1.56

1.56 * std error <5

Or 1.56(50)/rtn <5

rtn > 1.56(50)/5 = 15.6

n >243.36

n should be greater than 244.