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?

A. Finding for the 5th percentile

The 5th percentile simply means the 5th value from the lowest value. The total range of the sample value is:

range = x ± s

where x is the sample mean and s is the standard deviation

range = 203 ± 25.7

range = 177.3 days to 228.7 days

So the total is deviation range is:

total deviation = 228.7 - 177.3 = 51.4 days

5% of this plus the lowest range value is the 5th percentile:

5th percentile = 51.4 * 0.05 + 177.3

5th percentile = 179.87 days

B. The 3rd quartile is simple the value from the mean to one standard deviation away from the mean, hence:

3rd quartile range = x to x + s

3rd quartile range = 203 days to 203 + 25.7 days

3rd quartile range = 203 days to 228.7 days