Math, statistics...Given the population of men has normally distributed weights with a mean of 172 lb and a standard deviation of 29 lb?

a) if one man is randomly selected, find the probability that his weight is greater than 175 lb.

b) if 20 different men are randomly selected, find the probability that their mean weight is greater than 175 lb (so that their total weight exceeds the safe capacity of 3500 pounds).

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  • 4 months ago
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    a) P(x > 175) => P(z > (175 - 172)/29)

    i.e. P(z > 0.103)

    or, 1 - P(z < 0.103)

    From normal tables we have:

    1 - 0.5398 => 0.4602

    so, about 46%

    b) If we have a sample of n, our standard deviation becomes 29/√n

    i.e. 29/√20 => 6.48

    so, P(x > 175) => P(z > (175 - 172)/6.48)

    i.e. P(z > 0.46)

    or, 1 - P(z < 0.46)

    so, 1 - 0.6772 => 0.3228

    i.e. about 32%

    :)>

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