Question

Glenn Howell, vice president of personnel at Standard Insurance, has developed a new training program that is completely adaptable to the pace of users. New employees work in several stages at their own pace; the end of the training is when the material is learned. Howell's program has been especially effective in speeding up the training process, as an employee's salary during training is only 67% of what they would earn upon completion of the program. In recent years, the average program completion time has been 44 days, with a standard deviation of 12 days.

a) Find the probability of an employee completing the program between 33 and 42 days.

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

Answer 1

Solution :

Given that ,

mean = = 44  

standard deviation = = 12

(A)

P( 33 < x < 42)

= P[( 33 - 44 ) / 12 ) < (x - ) /  < (42 - 44 ) / 12 ) ]

= P( - 0.92 < z < -0.17 )

= P(z < - 0.17 ) - P(z < - 0.92 )

Using z table,

= 0.4325 - 0.1788

= 0.2537

Probability = 0.2537

(b)

P(x < 30 )

= P[(x - ) / < (30 - 44 ) / 12 ]

= P(z < - 1.17 )

Using z table,

= 0.1210

Probability = 0. 1210