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10 October, 19:10

Sheila's measured glucose level one hour after a sugary drink varies according to the normal distribution with μμ = 120 mg/dl and σσ = 20 mg/dl. what is the level l such that there is probability only 0.15 that the mean glucose level of 5 test results falls above l?

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  1. 10 October, 22:33
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    Since the sample size is below 30, in this case we use the t statistic. The formula for t score is:

    t = (x - u) / (σ / sqrt n)

    where,

    x = the level l = unknown

    u = sample mean = 120 mg / dl

    σ = standard deviation = 20 mg / dl

    n = sample size or number of results = 5

    Using the standard distribution tables for t, we can find the value of t given the probability (P = 0.15) and degrees of freedom (DOF).

    t = 1.036

    Going back to the formula for t score:

    1.036 = (x - 120) / (20 / sqrt 5)

    x = 129.27 mg / dl = l
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