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The daily high temperatures in Philadelphia for the first 15 days in February is normally distributed with a standard deviation of 2.5°. If it was 37° on Valentine's Day with a z-score of 2.4, the mean temperature is _________°.Immersive Reader

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Answer:

The mean temperature is 31.

Step-by-step explanation:

The formula for the z-sore is

          x - mean

z = ----------------------

        (std dev)

In this case let's multiply both sides by (std dev), obtaining:

x - mean = z*(std dev).

Solving for (mean), we get

mean = x - z*(std dev)

Substituing 37 for x, 2.4 for z and 2.5 for (std dev), we get:

mean = 37 - (2.4)(2.5) = 31

The mean temperature is 31.