Question 1194313
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mu = 63.7 = population mean height
n = 70 = sample size
sigma = 2.91 = population standard deviation of the heights
xbar = sample mean


We want to know the value of P(xbar > 64)


Let's find the z score for xbar = 64
z = (xbar - mu)/(sigma/sqrt(n))
z = (64 - 63.7)/(2.91/sqrt(70))
z = 0.86253610982893
z = 0.86


Use a table like this one
<a href = "https://www.ztable.net/">https://www.ztable.net/</a>
to find that
P(Z < 0.86) = 0.80511
which leads to
P(Z > 0.86) = 1-P(Z < 0.86)
P(Z > 0.86) = 1-0.80511
P(Z > 0.86) = 0.19489
which gets us back to
P(xbar > 64) = 0.19489
You can use a z calculator if you require more accuracy.


Answer: Approximately 0.19489
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