Question

In: Statistics and Probability

Weekly gross income earned by lecturers in XYZ University is normally distributed with a mean of...

Weekly gross income earned by lecturers in XYZ University is normally distributed with a mean of $1,600 and a standard deviation of $250. The Chief Operation Manager of XYZ University would like to do an audit on the weekly gross income earned by lecturers in his institution. Assist the manager is answering this: what is the probability that if 50 lecturers are randomly selected, their average weekly gross income would be more than $1,700?

a.

0.9954
b.

0.9977
c.

0.0023
d.

0.4977
e.

0.5023

Solutions

Expert Solution

Given that,

mean = = 1600

standard deviation = = 250

n=50

= =1600

= / n = 250/ 50 = 35.355

P( >1700 ) = 1 - P( < 1700)

= 1 - P[( - ) / < (1700-1600) /35.355 ]

= 1 - P(z <2.83 )

Using z table

= 1 - 0.9977

= 0.0023

orchestra answered 2 years ago
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