A Market Researcher for a Consumer Electronics Company Wants to Study the Weekly TV Viewing

Sp08 Math 227 FINAL Name:______

Show your work neatly, clearly, and systematically. Be reasonable in rounding your answers.

1. (16) Consider the following table. 2 2 a. (5) Extend the table to find  x ,  y ,  x ,  y ,  xy x y 12 15 17 12 18 11 3 19 6 17 8 18 20 11 14 15 16 13 9 16

b. (4) Compute Cov(X,Y), Var(X), and Var(Y).

c. (4) Compute Cor(X,Y) and the slope of the least-square line.

d. (3) Find the equation of the least-square line. 2. (17) Consider a box containing 10 identical balls except in color: 3 green, 5 yellow, and 2 red. a. (2) Three balls are selected at random. Find the probability that at most one red ball selected.

b. (5) Four balls are selected at random. Find the probability that at least one of each color is selected.

c. (4) Three balls are selected at random from each of twelve identical boxes, each as described above. Find the probability that the event of “at most one red ball” happens in at least 3 of those 12 experiments.

d. (6) Three balls are selected at random from each of 100 identical boxes, each as described above. Find the probability that the event of “at most one red ball” happens in at least 30 of those 100 experiments. 3. (14) The Supreme Court is widely considered to consist of 5 Justices with Republican platform and 4 Justices with Democrats platform. [For sake of simplicity, we will just say “5 Republicans” and “4 Democrats”]. Three of the Justices are invited to a White House luncheon. a. (8) Create a probability distribution.

b. (6) COPY and extend the probability distribution you have in part (a) to find the mean and standard deviation. 4. (15) The number of customers arrive at the pharmacy counter at a Ralph’s is, on average, 12 customers per hour. Suppose the number of arrivals follows Poisson distribution. USE TABLE. a. (3) Find the probability that there are more than 5 customers arriving in the next hour.

b. (3) Find the probability that there are less than 3 customers in the next 30 minutes.

c. (3) Find the probability that the next customer arrives after 20 minutes later.

d. (6) Suppose a survey is conducted for a period of 40 hours. Find the probability that the average number of customers per hours in survey is less than 11.5 customers per hour. Use Central Limit 2 Theorem. Note that if X ~ Poison, then  X   X   . 5. (15) Thomas’ Statistics class: 14 of 19 students are passing, class average score 70 with s.d. 22. Stephen’s Statistics class: 16 of 23 students are passing, class average score 67 with s.d. 18. a. (8) At 5%-SL, are the proportion of passing students in their classes equal?

b. (7) At 5%-SL, are their class averages equal? 6. (20) The following is the scores made by the 40 NBA top-scorers in this season.

30 22 21 20 28 22 21 20 a. (1) Median 26 22 21 20 26 22 20 19 b. (2) Mode 25 22 20 19 c. (1) Range 24 21 20 19 24 21 20 19 d. (2) Find the number of classes according to Sturge’s 23 21 20 19 Rule. 23 21 20 19 22 21 20 18

Source: NBA.com e. (2) Find the class width.

f. (8) Create a Frequency Distribution. And extend to find the approximate mean, variance, and standard deviation.

g. (4) Find the 98%-Confidence Interval for the average scores made by the next season 40 top-scorers. 7. (19) The chips of a computer manufacturer are supplied by 3 companies: 40% from A, 35% from B, and the rest by C. Of those supplied by A, 1% are defective; by B, 2% are defective; by C, 4% are defective.

a. (4) Construct the Tree Diagram of the situation.

b. (3) A chip is randomly selected. Find the probability that the chip is from A and defective.

c. (3) A chip is randomly selected. Find the probability that the chip is defective.

d. (3) Given a chip is defective. Find the probability that the chip is from A.

e. (6) Out of 100 defective chips, find the probability that less than 25 are from company A.