Respuesta :
Answer: approximately 0.1587
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Work Shown:
mu = 60 is the population mean
sigma = 5 is the population standard deviation
n = 90 is the sample size
Compute the z score for the raw score xbar = 60.527
z = (xbar-mu)/(sigma/sqrt(n))
z = (60.527-60)/(5/sqrt(90))
z = 0.527/(5/9.48683298050514)
z = 0.527/0.52704627669473
z = 0.999912196145243
z = 1.00
I'm rounding to two decimal places as this is common in many z tables.
So P(xbar > 60.527) is approximately the same as P(Z > 1.00)
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Use a z table to find that
P(Z > 1) = 1-P(Z < 1)
P(Z > 1) = 1-0.8413
P(Z > 1) = 0.1587
You can get a more accurate answer with a calculator (eg: the "normcdf" function on a TI83 or TI84); however, most stats books use tables to help make sure all students are on the same page (in terms of the final answer).
