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PracticeQuestions4 - Practice Questions 4 1 The amount of...

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Practice Questions 4 1. The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes. a. What is the probability that you have to wait more than 30 seconds for the light? A) 0.25 B) 0.50 C) 0.75 D) 1.01 b. What is the probability that you have to wait between 15 and 45 seconds for the light? A) 0.15 B) 0.25 C) 0.35 D) 0.45 c. Eighty percent of the time, the light will change before you have to wait how long? A) 90 seconds B) 24 seconds C) 30 seconds D) 96 seconds d. Sixty percent of the time, the light will change before you have to wait how long? A) 72 seconds B) 60 seconds C) 48 seconds D) 36 seconds 2. Let the random variable Z follow a standard normal distribution. a. What is P ( Z > 1.2)? A) 0.1112 B) 0.8849 C) 0.1151 D) 0.6112 b. What is P ( Z > -0.21)? A) 0.4207 B) 0.4168 C) 0.5793 D) 0.5832 c. What is P (0.33 < Z < 0.45)? A) 0.5443 B) 0.0443 C) 0.4557 D) 0.1515 1
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3. Let the random variable X follow a normal distribution with a mean of 17.1 and a standard deviation of 3.2. a. What is P ( X > 16)? A) 0.3401 B) 0.6331 C) 0.3669 D) 0.8326 b. What is P (15 < X < 20)? A) 0.5581 B) 0.1814 C) 0.5640 D) 0.2546 4. Let the random variable X follow a normal distribution with a mean of 61.7 and a standard deviation of 5.2. a. What is the value of k such that P ( X > k ) = 0.63? A) 59.984 B) 66.446 C) 62.830 D) 67.576 b. What is the value of k such that P (59 < X < k ) = 0.54? A) 65.8 B) 64.6 C) 63.7 D) 66.9 5. The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4. a. What is the probability that in a particular month the office receives more than 310 orders? A) 0.7823 B) 0.2826 C) 0.7174 D) 0.2177 b. The probability is 0.3 that the sales office receives less than how many orders? A) 310.9 B) 285.1 C) 290.0 D) 306.0 2
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6. Investment A has an expected return of 8% with a standard deviation of 2.5%. Investment B has an expected return of 6% with a standard deviation of 1.2%. Assume you invest equally in both investments and that the rates of return are independent. a. What is the expected return of your portfolio? A) 8% B) 7% C) 6% D) 4% b. What is the standard deviation of the return on your portfolio? Assume that the returns on the two investments are independent. A) 2.77 B) 1.40 C) 7.69 D) 6.25 7. The length of time it takes to be seated at a local restaurant on Friday night is normally distributed with a mean of 15 minutes and a standard deviation of 4.75 minutes. a. What is the probability that you have to wait more than 20 minutes to be seated? A) 0.1761 B) 0.3531 C) 0.6761 D) 0.1469 b. What is the probability that you have to wait between 13 and 16 minutes to be seated? A) 0.083 B) 0.246 C) 0.163 D) 0.663 c. Let the random variable Z follow a standard normal distribution. Find P (0 < Z < 0.57). A) 0.2843 B) 0.7843 C) 0.2157 D) 0.7157 d. Let the random variable Z follow a standard normal distribution. Find P (-2.21 < Z < 0).
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