SOLUTION: The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches, and a standard deviation of 10 inches. What is the probability that th
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-> SOLUTION: The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches, and a standard deviation of 10 inches. What is the probability that th
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Question 885649: The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches, and a standard deviation of 10 inches. What is the probability that the mean annual snowfall during 25 randomly picked years will exceed 72.8 inches? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! pm = population mean
psd = population standard deviation
n = sample size
se = standard error = standard deviation of the distribution of sample means
xm = sample mean
in this problem:
pm = 70
sm = 72.8
n = 25
psd = 10
se = psd / sqrt(n) = 10 / sqrt(25) = 10 / 5 = 2
z = (sm - pm) / se = (72.8 - 70) / 2 = 2.8 / 2 = 1.4
z factor of 1.4 gives you an area to the left of it of .9192 which means the area to the right of it is equal to 1 - .9192 = .0808.
since you want to know the probability that the z score is greater than 1.4, then you want the area to the right of it.
