Example of discrete random variable:

1. What is a discrete random variable? Give three examples from the field of business.

2. Of 1000 items produced in a day at XYZ Manufacturers, 400 are produced on the first shift, 350 on the second and 250 on the third. Suppose that the proportions of defective items produced on the first, second and third shifts are 0 01, 0.02, and 0.04, respectively. An item is picked at random. What is the probability that it was produced on (a) the first shift (b) either the first or the second shift? (c) What is the probability that it is defective? (d) What is the probability that it is defective, given that it was produced on the third shift? (e)What is the probability that it is defective and also was produced on the first shift?

3. ABC company has 2000 accounts receivable. The mean and standard deviation are $300 and $50, respectively. Assume that the accounts are normally distributed.

(a) How many accounts exceed $400?

(b) What is the probability that an account selected at random will be between $200 and $350?

(c) Forty percent of the accounts exceed what dollar amount?  (Hint: Fifty percent of the accounts are for more than $300.)

(d)  Twenty percent of  the accounts are below what dollar amount?

(4)  A manufacturer claims that 6% of her product is defective. If the claim is true what is the probability that the number of defective products in a random sample of 20 will be (a) exactly 2  (b) 2 or more  (c) 0  (d) fewer than 5  (e) between 2 and 5 inclusive?

(5) A government agency is conduction a check on label specifications for a product. Suppose that in a particular crate are 6 out of 24 cans whose contents do not meet their label specifications. The agency chooses 6 cans from a crate. What is the probability that the agency will find no mislabeled cans?

(6)  A sample of 80 costumers at 'ABC' Department Store were interviewed regarding their buying habits. One question asked was, " How many times did you shop at this store during the preceding month?" The responses are shown in the table that follows. (a) Find the probability that randomly selected customer shopped (1) more than once (2) zero times (3) more than four times (4) fewer than three times (b) Find the mean and variance.