A set of city temperatures in April are normally distributed with a mean of 19.7 degrees Celsius and a standard deviation of 2 degrees Celsi

Question

A set of city temperatures in April are normally distributed with a mean of 19.7 degrees Celsius and a standard deviation of 2 degrees Celsius. The average temperature in Cairo is 21.4 degrees Celsius.

What percentage of average city temperatures are higher than that of Cairo?

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Aubrey 2 weeks 2021-09-10T08:18:58+00:00 1 Answer 0

Answers ( )

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    2021-09-10T08:20:28+00:00

    Answer:

    19.77% of average city temperatures are higher than that of Cairo

    Step-by-step explanation:

    Problems of normally distributed samples are solved using the z-score formula.

    In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

    Z = \frac{X - \mu}{\sigma}

    The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

    In this question, we have that:

    \mu = 19.7, \sigma = 2

    What percentage of average city temperatures are higher than that of Cairo?

    This is 1 subtracted by the pvalue of Z when X = 21.4.

    Z = \frac{X - \mu}{\sigma}

    Z = \frac{21.4 - 19.7}{2}

    Z = 0.85

    Z = 0.85 has a pvalue of 0.8023

    1 – 0.8023 = 0.1977

    19.77% of average city temperatures are higher than that of Cairo

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45:7+7-4:2-5:5*4+35:2 =? ( )