Problem 1

Suppose that we check for clarity in 50 locations in Lake Tahoeand discover that the average depth of clarity of the lake is 14feet. Suppose that we know that the standard deviation for theentire lake's depth is 2 feet. What is the confidence interval forclarity of the lake with a 99% confidencelevel?   

Problem 2 Consider the following exercise:Suppose that a student is taking a multiple-choice exam in whicheach question has four choices. Assuming that she has no knowledgeof the correct answer to any of the questions, she has decided on astrategy in which she will place four balls (marked A, B, C, and D)into a box. She randomly selects one ball for each question andreplaces the ball in the box. The marking on the ball willdetermine her answer to thequestion.                                                                                                                 

1. If there are five multiple-choice questions on the exam, whatis the probability that she will get five questions correct?

1. What is the probability that she will get no more than twoquestions correct?

      (3) Problem 3   The average number of vehicle arrivalsat an intersection is five per minute. Find the probability thatthirteen vehicles arrive in 3 minutes.

       ( 4) Problem4 Researchers have conducted a survey of 1600 coffeedrinkers asking how much coffee they drink in order to confirmprevious studies. Previous studies have indicated that 72% ofAmericans drink coffee. The results of previous studies     

                                   Are provided in the survey below.