Assume the time spent (in days) waiting for a heart transplant for people ages 35-49 can be approximated by a normal distribution with mean of 203 days and a standard deviation of 25.7 days. what waiting time represents the 5th percentile? what waiting time represents the third quartile?

5th percentile = 160.852 days

3rd quartile = 220.22 days

Step-by-step explanation:

Let X be the random variable representing the waiting time.

Here the mean(\mu) = 203 days

Standard deviation (\sigma) = 25.7 days

For calculating the 5th percentile, we need to find the z- score having area 0.05.

By Z-score table we have Z= -1.64

Now, Using formula X=Z\sigma +\mu

X = (-1.64)*(25.7)+203

  = 160.852 days

Waiting time representing 5th percentile = 160.852 days.

For calculating third quartile, we know that third quartile represents the area to the left of 75% = 0.75

Hence, we need to calculate the Z score when the area is 0.75. Using the table we get Z= 0.67

X = (0.67)*(25.7)+203

   = 220.22 (days)

Waiting time representing third quartile = 220.22 days