Stat 1400 Test 2 Review(1)

STAT 1400 Statistical Concepts for Business Test 2 Review – Units 4-6 To earn full credit, show all work (including TI-83/84 commands) and round answers to the thousandths place (three decimals). Formulas on the last page. 1. A small manufacturing company recently instituted a new customer satisfaction training for its employees. Two methods of training were offered: online and face-to-face. Below is a table summarizing employees’ selections based on their department: Sales Product Developmen t Product Support Face-to-face 16 10 5 Online 35 23 47 (a) What is the probability that an employee chooses online training? (b) What is the probability an employee is in Sales and chooses online training? (c) What is the probability that an employee chooses online training given that he/she is in Sales? (d) Is it unusual for a Product Support employee to choose face-to-face training? Explain. (e) What is the probability that an employee chooses face-to-face instruction or is in Product Development? (f) Suppose two employees are randomly selected without replacement. What is the probability that both of them chose face-to-face instruction? (g) Suppose two employees are randomly selected without replacement. What is the probability that at least one of them chose face-to-face instruction? Columbus State Community College

2. Are we influenced to by buy a product by an ad we saw on TV? National Infomercial Marketing Association determined the number of times buyers of a product watched a TV infomercial before purchasing the product. The probability distribution is shown below: X = Number of Times Buyers Saw Infomercial before purchasing product 1 2 3 4 5 Probability P ( X ) 0.27 0.31 0.18 0.09 0.15 (a) Is the random variable X = number of times buyers saw the infomercial a discrete or continuous variable? Explain . (b) Do we have a valid probability distribution? Explain . (c) Find the probability that the buyer saw the infomercial at least three times before purchasing the product. (d) Find the mean (expected value) for this probability distribution. Interpret what the mean tells us in the context of this problem. (e) Find the standard deviation of the number of times buyers saw the infomercial before purchasing the product. 3. A company has determined that if a Senior Sales Representative is sent to a client’s place of business to demonstrate the product, a sale is produced 40% of the time. Suppose a random sample of six clients is selected for the Senior Sales Representative to demonstrate the product. 2

4. Find the following using the standard normal distribution. (a) P ( z < –2.05) (b) P (–1.96 < z < 1.96) (c) Find z such that 15% of the area under the standard normal curve lies to the left of z . (d) Find Z 0.20 . Draw the picture and show all work. 5. Suppose that the quarterly price of the stock of Company ABC is normally distributed with mean  =$2.0 and with standard deviation  = $1.20. Find the following: a. The quarterly price of Company ABC’s stock that has a z - score of 1 and interpret the result. b. The quarterly price of Company ABC’s stock that represents the 85 th percentile and explain what this value represents in context. c. What proportion of the quarterly price of Company ABC’s stock are between $1.19 and $2.81? 4

6. A politician in a close election race claims that 52% of the voters support him. A poll is taken in which 200 voters are sampled, and 44% of them support the politician. (a) Assume the claim is true. What is the mean and the standard deviation of the sampling distribution of sample proportions? (b) If the claim is true, what is the probability of obtaining a sample proportion that is less than or equal to 0.44? (c) If the claim is true, would it be unusual to obtain a sample proportion less than or equal to 0.44? Explain. (d) If the claim is true, would it be unusual for less than half of the voters in the sample to support the politician? 5

STAT 1400 Formulas for Test 2 : Probability P(A or B) = P(A) + P(B) – P(A and B) P(A and B) = P(A) * P(B) if A and B are independent events P(A and B) = P(A) * P(B|A) = P(B)*P(A|B) if A and B are dependent events P(complement of E) = 1-P(E) P(at least 1) = 1-P(none) P(A|B) = ( ) ( ) P AandB P B Discrete Random Variables: μ X = ∑ [ x∙ P ( x ) ] σ X 2 = ∑ [ ( x − μ X ) 2 ∙P ( x ) ] σ X = √ σ X 2 Binomial Random Variables: μ X = np σ X 2 = np ( 1 − p ) σ X = √ np ( 1 − p ) Standard deviation of the sample mean: σ ´ x = σ √ n Standard deviation of the sample proportion σ ^ p = √ p ( 1 − p ) n 7