Suppose Xi s are independent and identical random variables

Suppose X_i \'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 What is the distribution of X and explain how you got this answer. Find a 88% confidence interval for population mean. What sample size needed in order to estimate mu within plusminus 5 with 12% type 1 error? In a university library elevator there is a sign indicating a 16-person limit as well as a weight limit of 2500 lbs. Suppose (hat the weight of students, faculty, and staff is approximately Normally distributed with a mean weight of 150 lbs and a standard deviation of 27 lbs. When the elevator is full, we can think of the 16 people in the elevator as a simple random sample of people on campus What average weight for these 16 people in the elevator will result in the total weight exceeding the weight limit of 2500 lbs? What is the probability that the random sample of 16 people in the elevator will exceed the weight limit? What is the probability of exactly 4 groups will exceed the maximum weight limit. Suppose we selected a SRS of 12 groups (16 people in each) what is the probability, at most 25% of the groups will exceed the maximum weight limit.

Solution