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8. The high temperatures in Phoenix during the month of July are normally distributed with a mean of 106 and astandard deviation of 5º. Find the probability that on a given day in July the temperature is greater than 115º.Answer:

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The z-score formula is


Z=(x-\mu)/(\sigma)

In our case,


\begin{gathered} x=115,\mu=106,\sigma=5 \\ \Rightarrow Z=(9)/(5)=1.8 \\ \Rightarrow Z=1.8 \end{gathered}

Using a table for positive Z-scores, we find that


P(x\le115)=0.9641

Therefore,


P(x>115)=1-P(x\le115)=1-0.9641=0.0359

Then, the answer is 0.0359

User Frank Hoffman
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