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7 May, 08:37

A physical fitness association is including the mile run in its secondary - school fitness test. the time for this event for boys in secondary is known to process a normal distribution with a mean of 440 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in school can run the mile in less than 348 seconds

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  1. 7 May, 08:39
    0
    The probability that a randomly selected boy in school can run the mile in less than 348 seconds is 1.1%.

    Step-by-step explanation:

    1. Let's review the information provided to us to answer the question correctly:

    μ of the time a group of boys run the mile in its secondary - school fitness test = 440 seconds

    σ of the time a group of boys run the mile in its secondary - school fitness test = 40 seconds

    2. Find the probability that a randomly selected boy in school can run the mile in less than 348 seconds.

    Let's find out the z-score, this way:

    z-score = (348 - 440) / 40

    z-score = - 92/40 = - 2.3

    Now let's find out the probability of z-score = - 2.3, using the table:

    p (-2.3) = 0.0107

    p (-2.3) = 0.0107 * 100

    p (-2.3) = 1.1% (rounding to the next tenth)

    The probability that a randomly selected boy in school can run the mile in less than 348 seconds is 1.1%.
  2. 7 May, 09:07
    0
    0.0107

    Step-by-step explanation:

    z = (348 - 440) / 40 = - 2.3

    1 - 0.9893

    = 0.0107
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