Question
In: Statistics and Probability
A population of 40 year-old females has a mean salary of $39,321 with a standard deviation...
A population of 40 year-old females has a mean salary of $39,321 with a standard deviation of $2,120. If a sample of 100 women is taken:
a) What is the probability their mean salaries will be less than $39,000?
b) What is the probability their mean salaries will be between $38000 and $39,000?
Solutions
Expert Solution
Solution :
Given that ,
=
/ 
n = 2120 /
100 = 212
a)
P(
< $39000) = P((
- 
) /
< (39000 - 39321) / 212)
P(z < -1.51)
= 0.0655
Probability = 0.0655
b)
= P[(38000 - 39321) /212 < (
-
)
/
< (39000 - 39321) / 212)]
= P(-6.23 < Z < -1.51)
= P(Z < -1.51) - P(Z < -6.23)
= 0.0655 - 0
= 0.0655
Probability = 0.0655
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