Question

The time spent​ (in days) waiting for a kidney transplant for people ages​ 35-49 can be approximiated by the normal​ distribution, as shown in the figure to the right. ​(a) What waiting time represents the 90th ​percentile? ​(b) What waiting time represents the first​ quartile? μ = 1669 days σ = 210.8

Answer 1

Solution :

Given that,

mean =  = 1669

standard deviation =  = 210.8

P(Z < z) = 90%

P(Z < z) = 0.90

P(Z < 0.1282) = 0.90

z = 0.1282

Using z-score formula,

x = z * +

x = 0.1282 * 210.8 + 1669

x = 1696.02456

x = 1696

The 90th ​percentile is 1696

b ) The First Quartile

P(Z < z) = 255

P(Z < z) = 0.25

P(Z < 0.5987) = 0.25

z = 0.5987

Using z-score formula,

x = z * +

x = 0.5987 * 210.8 + 1669

x = 1795.20

x = 1795

The First Quartile is 1795