Question

The time spent​ (in days) waiting for a heart transplant for people ages​ 35-49 can be approximated by the normal​ distribution, as shown in the figure to the right. ​(a) What waiting time represents the 5th ​percentile? ​(b) What waiting time represents the third​ quartile? 207 307 107 Days mu equals 207sigma equals 24.1 x A normal curve labeled mu = 207 and sigma = 24.1 is over a horizontal x-axis labeled "Days" from 107 to 307 in increments of 50 and is centered on 207.

​(a) The waiting time that represents the 80th percentile is _ days. ​(Round to the nearest integer as​ needed.)

​(b) The waiting time that represents the first quartile is _ days. ​(Round to the nearest integer as​ needed.)

Answer 1

The waiting time follows a normal distribution with:
Mean = mu = 207 days
Standard Deviation = sigma = 24.1

a) 5th percentile, P(z<z0) = 0.05
From the z-table, z0 = -1.64
-1.64 = (W - 207)/24.1
W = 167 days

b) The third quartile: P(z<z0) = 0.75
z0 = 0.67
0.67 = (W-207)/24.1
W = 223 days

a) At 80th percentile, P(Z<Z0) = 0.80
z0 = 0.84 (from z-table)
0.84 = (W-207)/24.1
W = 227 days

b)At first quartile, P(Z<Z0) = 0.25
Z0 = -0.67
-0.67 = (W-207)/24.1
W = 191 days