for Prof washington only

MATH 175 Homework 4 Due in Class 10/12/2015

Read chapter 6 in the book.

1. Find the following probabilities:

a. P [z > 2.83] b. P [z < −3.29] c. P [1.12 < z < 2.29] d. P [−2.00 < z < 2.00]

2. An automobile dealer finds that the average price of a previously owned vehicle is 8,256 dollars. He decides to sell cars that would appeal to the middle 60 percent of the market in terms of price. Find the maximum and minimum prices of the cars the dealer will sell. The standard deviation is 1,150 dollars and we are assuming a normal distribution.

3. The average hospital stay for all diagnoses is 4.8 days. If we assume a normal distribution and variance of 2.1 days, then 10 percent of stays are longer than how many days? Thirty percent of stays are less than how many days?

4. The average cholesterol content of a certain brand’s eggs is 215 mg with a standard deviation of 15 mg.

a. If an egg is selected, find the probability that the cholesterol content will be greater than 269 mg. b. If a sample of 25 eggs is selected, find the probability that the mean of the sample will be larger than 220 mg.

5. Why would most of the sample means differ somewhat from the popula- tion mean?

6. The mayor of a small town estimates that thirty-five percent of the resi- dents in the town favor the construction of a municipal parking lot. If there are 350 people at a town hall meeting, find the probability that at least 100 favor construction of the parking lot. Based on your answer, is it likely that 100 or more people would favor the parking lot?

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