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Set of average city temperatures in April are normally distributed with a mean of 19.7°C and a standard deviation of 2°C. The average temperature of Cairo is 21.4°C. What proportion of average city temperatures are the higher than that of Cairo?

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Answer:

The answer is "19.77%"

Step-by-step explanation:

Given:

[tex]\mu = 19.7\\\\ \sigma = 2\\\\\to P(x >21.4 ) = 1 - P(x< 21.4)\\\\[/tex]

                        [tex]= 1 - [\frac{P(x -\mu)}{ \sigma }< \frac{(21.4-19.7)}{2}]\\\\= 1 - P(z < 0.85)\\\\= 1 - 0.8023\\\\=0.1977\\\\=19.77\%[/tex]

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