Question

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:

Answer 1

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