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Department of statistics

Midterm exam November 15, 2011

Form B

Name: | I.D. Number: |

Instructions:

* Write your name and student ID. * You have one hour and thirty minutes to complete the exam. * You may use a formula sheet and a calculator. No other outside materials are allowed. * There are seven problems in the exam. * Total score of points is 20.

Problem 1:(5 points) Multiple-choice questions:

Question 1: If A and B are mutually exclusive events, with P(A) = 0.6 and P(B) =0 .4, then P(A and B) is: a. 0.50 b. 0.00 c. 0.24 d. 1.00

Question 2: As the sample size, n, increases, what happens to the shape of the sampling distribution of the
(1/2 point)What is the probability that exactly 3 have profited from insider information?

b. (1/2 point)What is the probability that at least 3 have profited from insider information?

c. (1/2 point)Determine the expected number and the variance of the number of banks profited from insider information.

Problem 5: (3.5 points). A manufacturing process produces items whose weights are normally distributed, with a mean of 120 grams and standard deviation 10 grams. a. (1/2 point) What is the probability that the weight of a randomly selected item will be exactly 80 grams?

b. (1 point)What is the probability that the weight of a randomly selected item will be greater than 105 grams?

c. (1 point)What is the 3rd quartile of the items weight?

d. (1 point)A random sample of 25 items is selected, what is the probability that the sample average of weights is at most 123 grams?

Problem 6:(3 points). The high cost of health care is a matter of major concern for a large number of families. A random sample of 40 families selected from an area showed that they spend an average of \$110 per month on health care with standard deviation of \$24. a. (2.5 points)Find a 95% confidence interval for the true mean health care expenditure per month incurred by all families in that area. (Check the assumptions and interpret the interval)

b. (1/2 point)What sample size should be taken so that a 99% confidence interval will have a margin of error