. 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:

The probability that a call lasts less than 4 minutes  

 P(X<4) = P(Z<-1.25) = 0.1056

Step-by-step 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

[tex]Z= \frac{x-mean}{S.D} = \frac{4-6.5}{2} = -1.25[/tex]

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

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