# MATHEMATICS

Question 1. 1. A market research firm is investigating the appeal of three package designs. The table below gives information obtained through a sample of 200 consumers. The three package designs are labeled A, B, and C. The consumers are classified according to age and package design preference. A B C Total Under 25 years 22 34 40 96 25 or older 54 28 22 104 Total 76 62 62 200 If one of these consumers is randomly selected, what is the probability that the person prefers design B?

Question 2. 2. Let A be the event that a student is enrolled in an accounting course, and let S be the event that a student is enrolled in a statistics course. It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and accounting. Find the probability that a student is in accounting but not in statistics. (Points : 3) 0.15 0.70 0.25 0.12 0.60

Question 3. 3. If X and Y are mutually exclusive events, then if X occurs _______. (Points : 3) Y must also occur, Y cannot occur, X and Y are independent, X and Y are complements, A and Y are collectively exhaustive

Question 4. 4. The area to the right of the mean in any normal distribution is equal to _______. (Points : 3) the mean 1 , the variance,  0.5,  -0.5

Question 5. 5. If x is a normal random variable with mean 80 and standard deviation 5, the z-score for x = 89 is ________. (Points : 3)      1.8,  -1.8,  1.6,  -1.6,  8.0

Question 6. 6. Within a range of z scores from -1 to +1, you can expect to find _______ per cent of the values in a normal distribution. (Points : 3) 95, 99, 68, 34, 100

Question 7. 7. The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last more than 1100 hours? (Points : 3) 0.4772 0.9772,   0.0228,   0.5228,   0.5513

Question 8. 8. Completion time (from start to finish) of a building remodeling project is normally distributed with a mean of 200 workdays and a standard deviation of 10 workdays. To be 99% sure that we will not be late in completing the project, we should request a completion time of _______ work-days. (Points : 3) 211,  207,  223,  200,  250

Question 9. 9. Financial analyst Larry Potts needs a sample of 100 securities listed on either the New York Stock Exchange (NYSE) or the American Stock Exchange (AMEX). According to the Wall Street Journal’s “Stock Market Data Bank,” 2,531 NYSE securities and 746 AMEX securities were traded on the previous business day. Larry directs his staff to randomly select 77 NYSE and 23 AMEX securities. His sample is a ____________. (Points : 3) disproportionate systematic sample, disproportionate stratified sample, proportionate stratified sample, proportionate systematic sample , proportionate cluster sampling

Question 10. 10. Suppose 40% of a student population works part time. If a random sample size of 300 students is drawn from the population, then the probability that 44% or fewer of the samples work part time is _______. (Points : 3) 0.0793 0.4207 0.9207 0.9900 1.0000

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