SOLUTION: Assume that​ women's heights are normally distributed with a mean given by mu equals 64.3 in μ=64.3 in​, and a standard deviation given by sigma equals 3.1 in `
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Question 1106396: Assume that women's heights are normally distributed with a mean given by mu equals 64.3 in μ=64.3 in, and a standard deviation given by sigma equals 3.1 in σ=3.1 in.
(a) If 1 woman is randomly selected, find the probability that her height is less than 65 in.
(b) If 50 women are randomly selected, find the probability that they have a mean height less than 6565 in.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd
z< (65-64.3)/3.1=z < +0.23
that probability is 0.5893
The second one is divided by the standard error, which is 3.1/sqrt(50)
That quotient is 0.438
z < 0.7/0.4380 <1.60
That probability is 0.9450; much less likely to find an average >65.
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