SOLUTION: The mean height of women in a country (ages 20−29) is 63.7 inches. A random sample of 70 women in this age group is selected. What is the probability that the mean height f
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Question 1194313: The mean height of women in a country (ages 20−29) is 63.7 inches. A random sample of 70 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume σ=2.91.
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Part 1
The probability that the mean height for the sample is greater than 64 inches is enter your response here. Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
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 https://www.ztable.net/
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.
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