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Lera25 [3.4K]
2 years ago
6

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

egrees Celsius. The average temperature in Cairo is 21.4 degrees Celsius.
What percentage of average city temperatures are higher than that of Cairo?
Mathematics
1 answer:
Sati [7]2 years ago
6 0

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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