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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:

Respuesta :

The z-score formula is

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

In our case,

[tex]\begin{gathered} x=115,\mu=106,\sigma=5 \\ \Rightarrow Z=\frac{9}{5}=1.8 \\ \Rightarrow Z=1.8 \end{gathered}[/tex]

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

[tex]P(x\le115)=0.9641[/tex]

Therefore,

[tex]P(x>115)=1-P(x\le115)=1-0.9641=0.0359[/tex]

Then, the answer is 0.0359

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