Question

Glenn Howell, vice president of standard insurance staff, has developed a new training program fully adaptable to the pace of users. new employees work in several stages at their own pace of work; the training term is given when the material is learned. The Howell program has been especially effective in accelerating the training process, since the salary of an employee during training is only 67% of what he would earn when completing the program. in recent years, the average term of the program has been 44 days, with a standard deviation of 12 days.

a) Find the probability that an employee will finish the program between 33 and 42 days.

b) What is the probability of finishing the program in less than 30 days?

c) To finish it in less than 25 or more than 60 days?

d) find the probability that an employee ends the program between 46 and 54 days.

e) find the probability that an employee ends the program between 41 and 50 days.

f) what is the probability of not finishing the program in 47 days?

Answer 1

Average Term of Program is 44 days with Standard Deviation of 12 days.

We could assume Normality in this case and let , X be a R.V. denoting the time of completion of the course.

X ~ N (44 , 12² )    ( X - 44 )/ 12 ~ N (0,1)

Using the Standard Normal Tables , we compute the value of Z in each case .

Also, we use linear interpolation to compute Probabilities :

( f( x ) - f( x₁ ) ) / ( f( x₁ ) - f( x₂ ) ) = ( x- x₁ ) / ( x₁ - x₂ )

a ) P (finishing between 33 and 42 days ) = P ( 33 < X < 42 ) = 0.2541

b ) P (finishing in less than 30 days ) = P (X < 30 ) = 0.1216

c ) P (finishing in less than 25 or more than 60 days ) = P ( X < 25 or X > 60 ) = 0.14798

d ) P (finishing between 46 and 54 days ) = P (46 < X < 54 ) = 0.23127

e ) P (finishing between 41 and 50 days ) = P (41 < X < 50 ) = 0.29017

f ) P (Not finishing in 47 days ) = P (X > 47 ) = 0.40129

The calculations are shown in the image attached Herewith . 0