Question
In: Statistics and Probability
Yoonie is a personnel manager in a large corporation. Each month she must review 36 of...
Yoonie is a personnel manager in a large corporation. Each month she must review 36 of the employees. From past experience, she has found that one review takes her about 2.6 hours each to do on average, with a population standard deviation of 0.7 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let be the random variable representing the mean time to complete the 36 reviews. Assume that the 36 reviews represent a random set of reviews. Find the probability that the mean of a month's reviews will be between 2.3 and 2.9 hours.
Solutions
Expert Solution
Given that ,
mean = 
= 2.6
standard deviation = 
= 0.7
n = 36
= 2.6
= /
P(2.3< <2.9
) = P[(2.3-2.6) / 0.1167< (
-
) / < (2.9-2.6) /
0.1167)]
= P( -2.57< Z <2.57 )
= P(Z <2.57 ) - P(Z < -2.57 )
Using z table
=0.9949-0.0051
=0.9898
probability=0.9898
orchestra answered 2 years agoRelated Solutions
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