1. A warehouse contains 6 computer printers, 4 of which are defective. A company randomly selects 3 of the 6 printers to purchase. Let the random variable k be the number of defective printers in the sample a) (3 marks). Write down the probability distribution of k. b) (2 marks). What is the probability all 3 are defective? c) (1 marks). What is the mean of x? d) (2 marks). What is the variance of x?

2. The following data represent the scores for a sample of 10 students on a 20-point chemistry quiz: 16, 14, 0, 8, 12, 12, 9, 10, 15, and 13. a) (15 marks). Find mean, median, Q1, Q3 and the inter-quartile range, the sample variance and sample standard deviation. b) (2 marks) Find the z-score for the smallest value in the data. Comment on whether this is an outlier with reason.

3. It was estimated that on the average two cars pass through an intersection between 10 and 11 in the morning. Let x represent the number of cars passing through that intersection during this time. a) (2 marks). What is the probability distribution of x? b) (2 marks). What is the probability that only 2 cars have passed through that intersection? c) (2 marks). What is the probability that more than 7 cars passed through the intersection? d) (1 marks). What is he mean of x? e) (1 marks). What is the variance of x?

4. (6 marks). Suppose that P(A) = 0.6, P(B) = 0.7, and that events A and B are independent. a. Find P(A B) b. Find P(A B) c. Are the two events A and B mutually exclusive? Give reason.

5. An experiment can result in one or both of events A = Smoker and B = Female, with the joint probabilities shown in the table below. A person is selected at random. A B 0.40 0.15 0.35 0.10 a) (2 marks). Find the probability that the person is a smoker. b) (2 marks). Find the probability that the person is female. c) (4 marks). Find the probability that the person is either a smoker or a female or both. d) (4 marks). If the person is male, what is the probability he smokes?

6. Let x denote the weight gain in pounds per month for a calf. The probability distribution of x is shown below. a) (8 marks). Find A. Find the mean, variance and standard deviation of weight gain in pounds per month for a calf? b) (4 marks). What is P(x 5| x < 15)? Show your work. X p(x) 0 0.1 5 0.3 10 A 15 0.4

7. Suppose 40% of the TV sets in use in Canada on a particular night were tuned into game 7 of the Stanley Cup Playoffs. If we were to take a sample of 20 in-use TV sets that night. Let x be the random variable denoting the number of TV sets in use out of the 20 sets samples. a) (3 marks). What is the probability distribution of x? b)(3 marks). What is the probability exactly three were tuned to the Stanley Cup Playoffs? c) (3 marks). What is the probability 15 or more were tuned to the Stanley Cup Playoffs? d)(2 marks). Find the mean and the variance of the number of in-use TV sets tuned to the Stanley Cup Playoffs that night.

8. A distribution of measurements is approximately mound shaped with mean 50 and standard deviation 10 a) (2 marks) What percentage of the measurements will fall between 30 and 70? First draw a diagram. b) (2 marks) What percentage of the measurements will fall between 30 and 80? c) (2 marks) What might you say about a measurement 100