Statistics:

Please show your solutions in detail.

1. Forty-six percent of a population possesses a particular characteristic. Random samples are taken from this population. Determine the probability - (a) The sample size is 60 and the sample proportion is between .41 and .53.

2. What is the average length of a company's policy book? Suppose policy books are sampled from 45 medium-sized companies. The average number of pages in the sample books is 213, and the population standard deviation of 48. Use this information to construct a 98% confidence interval to estimate the mean number of pages for the population of medium-sized company policy books.

3. Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 randomly selected Americans. Suppose 714 of the sampled people replied that the environment is a major issue with them. Construct a 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them. What is the point estimate of this proportion?

4. According to Runzheimer International, the average cost of a domestic trip for business travelers in the financial industry is $1,250. Suppose another travel industry research company takes a random sample of 51 business travelers in the financial industry and determines that the sample average cost of a domestic trip is $1,192, with a sample standard deviation of $279. Construct a 98% confidence interval for the population mean from these sample data. Assume that the data are normally distributed in the population.

5. A national beauty spa chain wants to estimate the number of times per year a woman has her nails done at one of their spas if she uses one at least once a year. The chain's researcher estimates that, of those women who use a beauty spa at least once a year to get their nails done, the standard deviation of number of times of usage is approximately 6. The national chain wants the estimate to be within one time of the actual mean value. How large a sample should the researcher take to obtain a 98% confidence level?

6. Suppose the average client charge per hour for out-of-court work by lawyers in the state of Iowa is $125. Suppose further that a random telephone sample of 32 lawyers in Iowa is taken and that the sample average charge per hour for out-of-court work is $110. If the population variance is $525, what is the probability of getting a sample mean larger than $135 per hour?