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Math Help - Normal distribution question

  1. #1
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    Normal distribution question

    I can't seem to be able to understand word problems

    an applicant take a test . The time it normally distributed with mean time 60 minutes and standard deviation 8 minutes . Determine how much time an applicant should be given in general so 97 percent of them will be able to complete the test

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  2. #2
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    Re: Normal dist

    First step back and think about it. The mean time is 60, and you want to find the time that 97% of folks take less than. "97%" corresponds to a little more than 2 standard deviations above the mean, right? [Why?]
    So your answer will be a little less than 60 + 2 * 8 = 76...right?

    Here's a hint on the details:

    You want to find time T so that F(t) = prob(t < T) = 0.97.

    We know
    <br />
F(t) = \phi((t - \mu)/ \sigma)<br />

    So you want to solve
    <br />
0.97 = \phi((t - 60)/ 8)<br />
    for t.

    We know
    <br />
\phi(1.88) = 0.97<br />

    So you want to find t so that
    <br />
(t - 60)/ 8 = 1.88<br />
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  3. #3
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    Thumbs up Angel (BestSolution)

    Let x variable is normally distributed, represents the time.

    =60 and σ=8 are the mean and standard deviation of the time.

    So we have to find x1 where 97% students will be able to complete their test.

    So,

    z1 = (x1 - )/σ (z1 lies on z-axis corresponding x1 on x-axis)

    x1=+z1σ
    x1= 60+(1.88)(8) [z1 take from z-dist. Table]
    x1= 75.04 ~75
    x1= 75

    So if the time will be 75 min, then the students will be able to complete their test 97% complete.
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