46-Glenn Howell, vice president of staff for Standard Insurance, has developed a

Question

46-Glenn Howell, vice president of staff for Standard Insurance, has developed a new program Of training fully adaptable to the rhythm of the users. New employees work in Several stages at their own pace; The training term is given when the material is learned. Howell's program has been especially effective in accelerating the training process, Since an employee's salary during training is only 67% of what he would earn by completing the Program. In recent years, the program's average term has been 44 days, with a deviation Standard of 12 days.

A) Find the probability that an employee will complete 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?

Explanation / Answer

Assuming normal distribution with

Mean = 44 days

Standard deviation = 12 days

A) Probability that an employee will complete the program between 33 and 42 days = P(X < 42) - P(X < 33)

= P(Z < (42-44)/12) - P(X < (33-44)/12)

= P(Z < -0.17) - P(X < -0.92)

= 0.4325 - 0.1788

= 0.2537

B) Probability of finishing the program in less than 30 days = P(X < 30)

= P(Z < (30-44)/12)

= P(Z < -1.17)

= 0.1210

C) P(less than 25 or more than 60 days) = P(X < 25) + 1 - P(X < 60)

= P(Z < (25-44)/12) + 1 - P(Z < (60 - 44)/12)

= P(Z < -1.58) + 1 - P(Z < 1.33)

= 0.0571 + 1 - 0.9082

= 0.1489

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