Question

Patients wait 126 days on average for a heart transplant with a standard deviation of 24 days. Whatproportion waits fewer than 90 days? (enter theanswer as a percent rounded to the nearesthundredth as needed)

Answer 1

Answer:

6.68%

Explanation:

• Average Wait Period = 126 days

,

• Standard Deviation = 24 days

,

• X=90 days

First, we find the z-score using the z-score formula:

$\begin{gathered} z=\frac{X-\mu}{\sigma} \\ z=\frac{90-126}{24}=-\frac{36}{24}=-1.5 \end{gathered}$

Next, we find the proportion that waits fewer than 90 days, i.e. P(z<-1.5).

From the z-score table:

$\begin{gathered} P(z<-1.5)=0.066807 \\ =6.68\% \end{gathered}$

The proportion that waits fewer than 90 days is 6.68%.