Quiz 7 Solutions-3

# Quiz 7 Solutions-3 - STAT 225 Quiz 7 Monday April 6 2015...

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1 STAT 225, Quiz 7 Monday, April 6, 2015 Name (please print) ________________________ Class Time: _________________ Directions: You have 15 minutes to complete the quiz. Show all work to receive full credit. Instructors will not interpret questions for you. Write out the probability statement and show work. Use 4 decimal places in your answers . According to the Daily Fuel Report on AAA.com (for March 31, 2015) the average price for a gallon of regular gasoline in Indianapolis was \$2.355 with a standard deviation of \$0.049. Assume that the gasoline prices follow a Normal distribution. Let X be the price for a gallon of gasoline in Indianapolis. X~Normal( μ = 2.355, σ = 0.049) a) What is the probability that a randomly chosen gasoline customer in Indianapolis paid more than \$2.40 for a gallon of regular gasoline? (3 points) P(X > 2.40) = P(Z > 2.40−2.355 0.049 ) = P(Z > 0.9184) = 1 − Φ(0.92) = 1 0.8212 = 0.1788 b) What is the probability that the customer will pay between \$2.22 and \$2.30 per gallon? (5 points) P(2.22 < X < 2.30) = 𝑃 ( 2.22−2.355 0.049 ≤ 𝑍 ≤ 2.30−2.355 0.049 ) = 𝑃(−2.7551 ≤ 𝑍 ≤ −1.1224) = Φ(−1.12) − Φ(−2.76) = 0.1314 0.0029 = 0.1285 c) You are using your car for work purposes. In order to be reimbursed for gasoline, your employer requires you to buy gasoline at low cost. In fact, the employer wants you to find gasoline priced at the 15 th percentile or lower. What gasoline price in Indianapolis will ensure that you have met this goal? (4 points) Want to find to find c such that P(X < c) = 0.15 ----use Z-table to find that Φ(−1.04) ≈ 0.15 Then convert using 𝑧 = 𝑐−𝜇 𝜎 -1.04 = 𝑐−2.355 0.049 solve for c = \$2.3040 d) On March 31, you filled your gasoline tank in Indianapolis, but do not remember the price per gallon at that station. Your car gets 32 miles per gallon of gasoline, and you have a 300 mile trip to make. What is the average cost of the fuel you will use on this 300 mile trip? (3 points) Find E [ 300 32 ∗ 𝑋] = 9.375*2.355=\$22.0781 X~ 𝑁(𝜇, 𝜎 2 ) 𝑍~𝑁(0, 1) 𝑧 = 𝑥−𝜇 𝜎

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