# mathematics

 Question 28.28. If the wages of workers for a given company are normally distributed with a mean of \$15 per hour, then the proportion of the workers earning more than \$13 per hour: (Ch7) (Points : 12)

Is less than the proportion earning less than \$13 per hour
Is equal to the proportion earning less than \$13 per hour
Is greater than the proportion earning less than \$13 per hour
Is less than 50%
Cannot tell from the information given.

 Question 29.29. In a study conducted by UCLA, it was found that 25% of college freshmen support increased military spending. If 6 college freshmen are randomly selected, find the probability that: “fewer than 4 support increased military spending” (Ch6) (Points : 12)

0.9624
0.9954
0.7844
0.0330

 Question 30.30. When the level of confidence and the sample size remain the same, a confidence interval for a population mean µ will be ________________, when the sample standard deviation s is smaller than when s is larger.  (Ch9) (Points : 12)

Wider
Narrower
Sometimes wider, sometimes narrower.
They will be the same

 Question 31.31. Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. One item is drawn from each container: What is the probability that one of the items is defective? (Hint: you have to use both rule of addition and rule of multiplication/conditional probability rules) (Ch5) (Points : 25)

 Question 32.32. Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25% for University A and 40% for University B. What is the probability that Joe will be accepted at one and only one university? (Ch5) (Points : 25)

 Question 33.33. The probability that an appliance is in repair is .5. If an apartment complex has 100 such appliances, what is the probability that at least 60 will be in repair? Use the normal approximation to the binomial. (Ch7) (Points : 25)

 Question 34.34. The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 10%. If 100 calculators are selected at random, what is the standard deviation of the number of defectives? (Ch6) (Points : 25)

 Question 35.35. A random sample of size 36 from a normal population yields  mean X-bar = 32.8 and standard deviation s = 4.51. Construct a 95 percent confidence interval for μ. (Ch9) (Points : 25)

 Question 36.36. Employees of a local university have been classified according to gender and type of job as follows: Job                       Male         Female Faculty                    110            10 Salaried staff             30             50 Hourly staff               60            40 If an employee is selected at random, what is the probability that the employee is a female or works as an hourly staff?  (Ch5) (Points : 25)

 Question 37.37. A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has been frequently failing and requiring repairs and service. The company has been able to provide its customers with a completion time of 6 days or less. To analyze whether the completion time has increased, the production manager took a sample of 25 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days. At a significance level of .05, test whether the completion time has increased. (form the hypotheses, show the critical and calculated values of the test statistic and perform the test)  (Ch10) (Points : 25)

 Question 38.38. An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that: Fewer than two troubles will be repaired on the same day? (Ch6)

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