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26 September, 19:18

Temperatures in June in the Paradise City are distributed nearly normally with mean 82 degrees and standard deviation 6 degrees F. Which of the following temperatures would be considered unusual?

A. 89.2

B. 75.4

C. 79

D. 86.2

E. 95.8

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  1. 26 September, 19:34
    0
    E

    Explanation:

    We are given, mean μ = 82°

    standard deviation σ = 6°

    For each of the options x, we will evaluate their respective z-scores given by

    z-score = (x - μ) / σ

    Hence, for 89.2, z = (89.2 - 82) / 6 = 1.2

    For 75.4, z = (75.4 - 82) / 6 = - 1.1

    For 79, z = (79 - 82) / 6 = - 0.5

    For 86.2, z = (86.2 - 82) / 6 = 0.7

    For 95.8, z = (95.8 - 82) / 6 = 2.3

    The z score of temperature greater than 2 and less than - 2 are considered as unusual

    This is the case with temperature 95.8°. Hence, the temperature will be considered unusual.
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