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14 April, 11:44

Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 46 days and a standard deviation of 10.5 days. Find the probability that a simple random sample of 49 protozoa will have a mean life expectancy of 47 or more days.

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  1. 14 April, 13:04
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    Answer: P (x ≥ 47) = 0.25

    Step-by-step explanation:

    Since the distribution of the life expectancies of a certain protozoan is normal, we would apply the formula for normal distribution which is expressed as

    z = (x - µ) / σ

    Where

    x = life expectancies of the certain protozoan.

    µ = mean

    σ = standard deviation

    n = number of samples

    From the information given,

    µ = 46 days

    σ = 10.5 days

    n = 49

    The probability that a simple random sample of 49 protozoa will have a mean life expectancy of 47 or more days is expressed as

    P (x ≥ 47) = 1 - P (x < 47)

    For x = 47

    z = (47 - 46) / (10.5/√49) = 0.67

    Looking at the normal distribution table, the probability corresponding to the z score is 0.0.75

    P (x ≥ 47) = 1 - 0.75 = 0.25
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