Given the population mean, μ = 45, and the population standard deviation, σ = 15 with a sample size of, n = 100.n = 100. Determine P ( x ¯ ≤ 42 ). To do this problem first determine the sampling mean and the sampling standard deviation in order to convert to a z-score. Round your answer to 4 decimals.
Solution :
Given that,
mean =
= 45
standard deviation =
=15
n = 100
= 45
=
/
n = 15 /
100=1.5
P(
< 42) = P[(
-
) /
< (42-45) /1.5 ]
= P(z < -2)
Using z table
probability= 0.9772
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