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    Probability Questions 2B

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    11. Which probability is greater? A: Prob (person is a CEO of a company | person is a male). B: Prob (person is a male | person is a CEO of a company)
    a. A b. B c. equally likely

    12. The number of raisins in boxes of cereal is normally distributed with a mean of 112 and a standard deviation of 15 raisins. Using the table, what is the probability that a box will have less than 132 raisins in it.
    a. 95% b. 41% c. 84% d. 91
    b.
    13. A die is rolled 3,000 times and the number of 5's and 6's together is noted. What is the approximate probability that the total number of 5's and 6's together is greater than 1,052? (This is a binomial situation; a roll results in a 5 or a 6, or it doesn't. Approximate it with a normal distribution and use its standard deviation.)
    a. 13.5% b. 16% c. 2.5% d. .015%

    14. Factory I produces 40% of the light bulbs in a certain country. Factory II produces 50% and Factory III produces the remaining 10% of them. If 2% of Factory I's light bulbs are defective, 4% of Factory II's light bulbs are defective, and 12% of Factory III's bulbs are defective, what percent of all the light bulbs are defective?
    a. 3.2% b. 4.0% c. 2.8% d. 4.2%

    15. If a light bulb is randomly selected and found to be defective, what is the probability it was produced by Factory III?
    a. 22.2% b. 18.6% c. 30.0% d. 38.2%

    16. For a random variable X with mean μ and standard deviation σ, the standard normal z is equal to
    a. (X-σ)/μ b. (X-μ)/σ c. (X-μ)/(σ^2) d. μX/σ

    17. Pick three numbers at random between 1 and 100 inclusive. What is the probability they're all are between 71 and 82 inclusive.
    a. .36 b. .001728 c. .363 d. none of these

    18. Roll a pair of dice. If you win $100 for rolling a 12, win $10 for rolling a number less than 7, and lose $4 for rolling anything else, what are your expected winnings per play? What are your expected winnings if you play this game 500 times?
    a. $1.94 b. $4.72 c. $2.88 d. -$.68

    19. Spin a dial 20 times. If the probability of landing on the A sector is .20, and the probability of landing on the B sector is .55, and the probability of landing on the C sector is .25, what is the probability of landing A 4 times, on B 11 times, and C 5 times?
    a. [20!/(4!11!5!)].204.5511.255 b. .20*4*.55*11*.25*5 c. Not enough info

    20. Scores on a test are normally distributed with mean 500 and standard deviation 50. What is the probability a score will be between 520 and 550?
    a. 19.8% b. 18.6% c. 24.1% 15.2%

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    Solution Preview

    11. Which probability is greater? A: Prob (person is a CEO of a company | person is a male). B: Prob (person is a male | person is a CEO of a company)
    a. A b. B c. equally likely

    Most CEOs are male, but most males are not CEOs.

    12. The number of raisins in boxes of cereal is normally distributed with a mean of 112 and a standard deviation of 15 raisins. Using the table, what is the probability that a box will have less than 132 raisins in it.
    a. 95% b. 41% c. 84% d. 91%

    z = (132 - 112) / 15 = 1.33
    From the table, this is 91%.

    13. A die is rolled 3,000 times and the number of 5's and 6's together is noted. What is the approximate probability that the total number of 5's and 6's together is greater than 1,052? (This is a binomial situation; a roll results in a 5 or a 6, or it doesn't. Approximate it with a normal distribution and use its standard deviation.)
    a. 13.5% b. 16% c. 2.5% d. .015%

    n = 3000
    p = 2/6 = 1/3
    q = 4/6 = 2/3

    mean = np = 3000 * 1/3 = 1000 ...

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