27)
The mean salary of people living in a certain city is $37,500 with a standard deviation of $1,614. A sample of 49 people is selected at random from those living in the city.
Find the probability that the mean income of the sample is less than $38,000.
Round your answer to 4 decimal places.
Please explain each step in detail.
Solution :
Given that ,
mean =
= $37500
standard deviation =
= $1614
=
/
n = 1614 /
49 = 230.5714
P(
< $38000) = P((
-
) /
< (38000 - 37500) / 230.5714)
= P(z < 2.1685)
= 0.9849
Probability = 0.9849
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