Question

Yoonie is a personnel manager in a large corporation. Each month she must review the employees in her department. From past experience, she has found that the reviews take her approximately four hours each to do with a standard deviation of 1.2 hours.

(1)  What is the mean time to complete one review?

2) How long in average it takes to complete two reviews?

(3) What is the probability that one review will take Yoonie from 3.5 to 4.25 hours? (Round to 3 decimal places)

(4) What is the probability that one review will take Yoonie from less than 2.8 hours? (Round to 2 decimal places)

5) What is the probability that one review will take Yoonie more than 6.4 hours? (Round to 3 decimal places)

(6)What is the probability that one review will take Yoonie fmore than 6.4 hours given that it took her more than 5.2 hours? (Use conditional probability and empirical rule.  Round to 3 decimal places) (Round to three decimal places)

Answer 1

1)mean time to complete one review =4 hours

2)average it takes to complete two reviews=2*4 =8 hours

3)

probability =P(3.5<X<4.25)=P((3.5-4)/1.2)<Z<(4.25-4)/1.2)=P(-0.42<Z<0.21)=0.5832-0.3372=0.246

4)

probability =P(X<2.8)=(Z<(2.8-4)/1.2)=P(Z<-1)=0.16

5)

probability =P(X>6.4)=P(Z>(6.4-4)/1.2)=P(Z>2)=1-P(Z<2)=1-0.9772=0.025

6)

P(X>6.4|X>5.2) =P(Z>((6.4-4)/1.2)/P(Z>(5.2-4)/1.2) =P(Z>2)/P(Z>1 )=0.025/0.16 = 0.156