Question

Problem 1

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

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

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

2. What is the probability that she will get no more than two questions correct?

      (3) Problem 3    The average number of vehicle arrivals at an intersection is five per minute. Find the probability that thirteen vehicles arrive in 3 minutes.

       ( 4) Problem 4 Researchers have conducted a survey of 1600 coffee drinkers asking how much coffee they drink in order to confirm previous studies. Previous studies have indicated that 72% of Americans drink coffee. The results of previous studies      

                                    Are provided in the survey below.

Answer 1

1:

2:

Let X is a random variable shows the number of correct answers. Here X has binomial distribution with following parameters

n=5 and p = 1/4 = 0.25

The probability that she will get five questions correct is

The probability that she will get no more than two questions correct is

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3:

Let X is a random variable showsthe number of vehicles arrive in 3 minutes. Here X has Poisson distribution with parameter

The  probability that thirteen vehicles arrive in 3 minutes is

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