Anonymous
Anonymous asked in Science & MathematicsMathematics · 5 months ago

Math Homework Help?

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.7 minutes and a standard deviation of 2.1 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes

(b) longer than 5 minutes

(c) between 8 and 15 minutes

Update:

Statistics Math Homework

1 Answer

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  • 5 months ago

    The first step is converting each raw score into a z-score. The z-score represents how many standard deviations the raw score is away from the mean.

    PART A:

    10 minutes is 0.3 minutes above the mean.

    10 - 9.7 = 0.3

    Divide by the standard deviation to find that we are about 1/7 of a standard deviation above the mean.

    z = 0.3 / 2.1

    z = 1/7

    z ≈ 0.143

    Use your calculator or your table to figure out P(z < 0.143)

    PART B:

    5 minutes is below the mean:

    5 - 9.7 = -4.7

    Divide by the standard deviation to get the z-score.

    z = -4.7 / 2.1

    z ≈ -2.238

    Use your calculator or your table to figure out P(z > -2.238)

    PART C:

    The raw scores are 8 and 15.

    8 minutes:

    z1 = (8 - 9.7) / 2.1

    z1 = -1.7 / 2.1

    z1 ≈ -0.81

    15 minutes:

    z2 = (15 - 9.7) = 5.3

    z2 = 5.3 / 2.1

    z2 ≈ 2.52

    You want to calculate P(-0.81 < z < 2.52)

    If you want to double-check your answers, use the following online calculator.

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