%3D Name: Mean, Variance, and Expectation 1. From past experience, a company has found that in carton of transistors, 92% contain no defective transistors, 3% contain one defective transistor, 3% contain two defective transistors, and 2% contain three defective transistors. a. Construct a probability distribution below. (X) b. Calculate the mean, variance, and standard deviation for the defective transistors. The Bank of America VP feels that each savings account customer has, on average, three credit cards. The following distribution represents the number of credit cards people own. X 0 1 2 3 4. P(X) 0.18 0.44 0.27 0.08 0.03 a. Find the mean, variance, and standard deviation. %3D b. Is the VP correct? Name: 3. Rish Florist determines the probabilities for the number of flower arrangements they deliver each day. 6 7 8 9 10 9. 0.2 0.2 0.3 0.2 0.1 (X) a. Find the mean, variance, and standard deviation. b. Approximately how many arrangements should Rish expect to deliver each week? Games & Expectation 1. A box contains ten $1 bills, five $2 bills, three $5 bills, one $10 bill, and one $100 bill. A person is charged $20 to select one bill. Find the expected value for this game. Is this game fair? 2. If a person rolls doubles when he tosses two dice, he wins $5. The cost to play the game is $1. Is this game fair?

A study of automobile accidents produced the following data: Proportion of all vehicles Probability of involvement in an accident Model year 2014 0.16 0.05 2013 0.18 0.02 2012 0.20 0.03 Other 0.46 0.04 An automobile from one of the model years 2014, 2013, and 2012 was involved in an accident. Calculate the probability that the model year of this automobile is 2013 (round to the nearest tenth).

Create different portfolios with weights (weightS&P, weightBond) where weightBond = 1 weightS&P. Let weightS&P equal 0%, 10%, 20%, 100%. Calculate the average return and the standard deviation for each of the eleven portfolios. Which of the following portfolio has the lowest risk (as measured by the standard deviation) ? The portfolio with 0% weight in the S&P500. The portfolio with 20% weight in the S&P500. The portfolio with 40% weight in the S&P500. The portfolio with 60% weight in the S&P500.

The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 46 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. inches inches 39.9 40.6 41.3 42 42.7 43.4 44.1 19.9 20.6 21.3 22 22.7 23.4 24.1 inches - 2.1 -1.4 -0.7 0 0.7 1.4 2.1 inches 10 14 18 22 26 30 34 (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.) (c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)