Question

The total cholesterol values for a certain population are approximately normally distributed with a mean of mg/100ml and a standard deviation of 20mg/100ml.

Find thetotalcholesterol valuescorresponding to the first quartile,thesecond quartileand the third quartilefor thispopulation.

Answer 1

Solution :

mean = = 100

standard deviation = = 20

Using standard normal table,

(a)

P(Z < z) = 0.25

P(Z < -0.67) = 0.25

z = -0.67

Using z-score formula,

x = z * +

x = -0.67 * 20 + 100 = 86.6

First quartile = 86.6

Second quartile = mean = 100

Because the normal distribution is symmetric .

P(Z < z) = 0.75

P(Z < 0.67) = 0.25

z = 0.67

Using z-score formula,

x = z * +

x = 0.67 * 20 + 100 = 113.4

Third quartile = 113.4