Question

Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately 4 hours each to do with a population standard deviation of 1.6 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews. Find the probability that the mean of a month's reviews will take Yoonie from 3.8 to 4.2 hrs.

(b) Express the probability statements for the sample mean as well as for the standard normal Z and find the probability. Use four decimal places.

P(__3.8__<X<__4.2__)=

P(___<Z<_____)=_____

Answer 1

Solution :

Given that,

mean = = 4

standard deviation = = 1.6

n = 16

= = 4

= / n = 1.6 / 16 = 0.4

P( 3.8 <   < 4.2 )  

= P[(3.8-4) /0.4< ( - ) / < (4.2-4) /0.4 )]

= P( -0.5 < Z < 0.5 )

= P(Z <0.5) - P(Z <-0.5 )

= 0.6915 - 0.3085 = 0.3829

probability = 0.3829