Question

the cholesterol levels of an adult can be described by a normal model with a mean of 199 ​mg/dL and a standard deviation of 28.

what's the IQR

Answer 1

Solution:-

Given that,

mean = = 199

standard deviation = = 28

Using standard normal table,

The z dist'n First quartile is,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.6745 ) = 0.25

z = -0.6745

Using z-score formula,

x = z * +

x = -0.6745 * 28 + 199

x = 180.11

First quartile =Q1 = 180.11

The z dist'n Third quartile is,

P(Z < z) = 75%

= P(Z < z) = 0.75  

= P(Z < 0.6745 ) = 0.75

z = 0.6745

Using z-score formula,

x = z * +

x = 0.6745 * 28 + 199

x = 217.89

Third quartile =Q3 = 217.89

IQR = Q3 - Q1

IQR = 217.89 - 180.11

IQR = 37.78