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 9898th ​percentile? ​(b) What waiting time represents the first​ quartile?

Mean= 1665

Standard deviation= 213.6

Round to the nearest integer as needed

Answer 1

Solution:-

Given that,

mean = = 1665

standard deviation = = 213.6

Using standard normal table,

a )P(Z < z) = 98%

= P(Z < z) = 0.98  

= P(Z < 2.054 ) = 0.98  

z =2.05

Using z-score formula,

x = z * +

x = 2.05 * 213.6 + 1665

x = 2102.88

98^th ​percentile = 2103

b ) P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.6745 ) = 0.25

z = -0.67

Using z-score formula,

x = z * +

x = -0.67 * 213.6 + 1665

x = 1521.89

First quartile =Q₁ = 1522