1. An aptitude test was given to a random sample of 228 people intending to become data-entry clerks. The results are shown below, where x is the score on a 10-point scale and f is the frequency of people with this score.

x 1 2 3 4 5 6 7 8 9 10 f 9 21 46 51 42 18 12 10 8 5

Assume that these data represent the entire population of people intending to become data-entry clerks.(a) Use the relative frequencies to find P(x) for x = 1 to x = 10. (b) Compute the probability that x is between 2 and 5 (including 2 and 5).(c) Compute the probability that x is less than 3.(d) Compute the expected value of the x distribution.(e) Compute the standard deviation of the x distribution.

10.Operating temperatures of two models of portable electric generators follow a normal distribution. For generator I, the mean temperature is 1 = 148F with standard deviation 1 = 25F. For generator II, the mean temperature is 2 = 143F with standard deviation 2 = 8F. At peak power demand, generator I was operating at 166F, and generator II was operating at 165F.

(a) At peak power output, both generators are operating at about the same temperature. Relative to the operating characteristics, is one a lot hotter than the other? Explain.

(b) Convert the peak power temperature for each generator to standard z units. Then locate both z scores under a standard normal curve. Could one generator be near a meltdown? Which one? Explain your answer.

13.A random sample of 14 evenings (6 to 9 P.M.) at the O'Sullivan household showed the family received an average of x = 5.2 solicitation phone calls each evening. The sample standard deviation was s = 1.9.

(a)Find a 95% confidence interval for the population mean number of solicitation calls this family receives each night.

14. Jordan is the manager of a used book store. He wants to estimate the average amount a customer spends per visit. A random sample of 80 customer receipts gave a mean of x = $6.90 with standard deviation s = $2.45.

(a) Find a 90% confidence interval for the average amount spent by all customers.

(b) What conditions are necessary for your calculations?

(c) For a day when the book store had 80 customers, use part (a) to estimate a range of dollar values for the total income on that day.

15.Mr. Crandall has assigned a term paper due at the end of the semester. He would like to know the average length of the paper. The data below are the numbers of typed pages from a random sample of 10 term papers. Create a 95% confidence interval for the population mean length of all term papers for his class.

14 20 25 10 16

8 15 12 18 9