Question

. The length of the long-distance calls made by the employees of a company followed a normal distribution with a mean of 6.5 minutes and a standard deviation of 2 minutes. a. What is the probability that a call lasts less than 4 minutes

Answer 1

The probability that a call lasts less than 4 minutes

P(X<4) = P(Z<-1.25) = 0.1056

Explanation:

Step(i):-

Given mean of the population = 6.5 minutes

Given standard deviation of the Population = 2 minutes

Let 'X' be the random variable in normal distribution

Given X = 4

`Z= (x-mean)/(S.D) = (4-6.5)/(2) = -1.25`

Step(ii):-

The probability that a call lasts less than 4 minutes

P(X<4) = P(Z<-1.25)

= 1-P(z>1.25)

= 1 - ( 0.5 +A(1.25)

= 1-0.5 - A(1.25)

= 0.5 - 0.3944 ( from normal table)

= 0.1056

Final answer:-

The probability that a call lasts less than 4 minutes

P(X<4) = P(Z<-1.25) = 0.1056