Answered

A set of average city temperatures in May are normally distributed with a mean of 20.66 ^\circ \text{C}20.66

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C20, point, 66, degrees, start text, C, end text and a standard deviation of 2 ^\circ \text{C}2

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C2, degrees, start text, C, end text. The average temperature of Singapore is 26 ^\circ \text{C}26

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C26, degrees, start text, C, end text.

What proportion of average city temperatures are lower than that of Singapore?

You may round your answer to four decimal places.

Answer :

raphealnwobi

Answer:

0.9962

Step-by-step explanation:

The z score shows the number of standard deviations by which the raw score is above or below the mean. If the raw score is above the mean then the z score is positive but if the raw score is less than the mean then the raw score is negative. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma}\\ \\\mu=mean,\sigma=standard\ deviation, x=raw\ score[/tex]

μ = 20.66°C, σ = 2°C

For x < Singapore temperature, i.e. x < 26

[tex]z=\frac{x-\mu}{\sigma} =\frac{26-20.66}{2}=2.67[/tex]

From the normal distribution table P(x < 26) = P(z < 2.67) = 0.9962

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