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PROJECT

Chapter 6

1. The life span of a calculator manufactured by “XXX” Corporation has a normal distribution with a mean of 54 months and a standard deviation of 8 months. The company guarantees that any calculator that starts malfunctioning within 36 months of the purchase will be replaced with a new one. About what percentage of such calculators made by this company are expected to be replaced?

2. Suppose the examination scores are normally distributed with a mean of 76 and a standard deviation of 15. The top 15% of the students receive A’s and the bottom 10% receive F’s. Find the minimum score needed to receive an A and the minimum score needed to pass (not to receive an F).

3. An International Revenue Oversight Board survey found that 80% of taxpayers said that it was very important for the Internal Revenue Service to ensure that high-income tax payers do not cheat on their tax returns. Use a normal distribution as an approximation to the binomial distribution if the requirements are satisfied. .

a) For the sample of 100 taxpayers, what is the probability that 90 taxpayers say that it is very important to ensure that high-income tax payers do not cheat on their tax returns?

b) For the sample of 100 taxpayers, what is the probability that at least 90 taxpayers say that it is very important to ensure that high-income tax payers do not cheat on their tax returns?

Chapter 7

4. You have been hired by a college foundation to conduct a survey of graduates.

If you want to estimate the percentage of graduates who made a donation to the college after graduation, how many graduates must you survey if you want 98% confidence that your percentage has a margin of error of 5 percentage point?

5. In a survey of 1003 people, 59% said that they have never hesitated to give a handshake because they had fear of germs. The survey results were reported in USA Today, and the survey is conducted by Wakefield Research for Purell, a supplier of hand sanitizer products.

a) Construct a 95% confidence interval estimate of the proportion of people in the population who have never hesitated to give a handshake because of a fear of germs.

b) Is there anything about the survey that might make the results questionable?

6. A retired statistics professor has recorded final exam results for decades. The mean final exam score for the population of her students is 82.4 with a standard deviation of 6.5. In the last year, her mean seems to have changed. She bases this on a random sample of 25 students whose final exam scores had a mean of 80 with a standard deviation of 4.2 Test the professor’s claim that the current mean is different using .05 level of significance.