Question

if 25% of the observations are less than 24.67 and 25%of the observations are more than 56.33 in the Normal distributions , what is coefficient of variance​

Answer 1

Given:

25% of the observations are less than 24.67

25% of the observations are less than 24.67

To find:

Coefficient of variance​

Solution:

Mean = Sum of observation / Total number of observations

According to the question,

(56.33 + 24.67) /2 = 40.5

P(x< 24.67) = 0.25

P(z< Z) = 0.25

P(z< -0.67) = 0.25143

P(z< -0.68)= 0.24825

From Z table,

-0.68 + 0.01* (0.25 - 0.24825) /(0.25143 -0.24825)

= -0.674496855

 Hence, Z for 0.25 = -0.6745

so

-0.6745 = ( X - mean ) /standard deviation

-0.6745 = ( 24.67 -40.5 ) /standard deviation

-0.6745 = -15.83/ standard deviation

 0.6745 *standard deviation = 15.83

Standard deviation = ( 15.83) / 0.67=23.48

CV = standard deviation / mean = 23.48/40.5 = 0.579

Hence, the coefficient of variation is 0.579