Question

Suppose that resting pulse rates among healthy adults are normally distributed with a mean of 78 beats per minute and a standard deviation of 10 beats per minutes. Find the percentage of healthy adults who have a resting pulse rates that are less then 64 beats per minute. For your intermediate computation, use four or more decimal places. Give your final answer to two decimal places ( for example 98.23%)

Answer 1

The Solution:

Given:

`\begin{gathered} \mu=78 \\ \\ \sigma=10 \\ \\ x=64 \end{gathered}`

By Z-statistic formula:

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

Substitute:

`Z=(64-78)/(10)=(-14)/(10)=-1.4`

From the Z-scores tables:

`P(Z<-1.4)=0.0808`

Converting to percentage, multiply by 100 to get:

`0.0808*100=8.08\text{ \%}`

Therefore, the correct answer is 8.08%