Question 1172750
Probability the mean height is less than 72 inches:
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z1 = {{{(72-71)/(1/sqrt(8))}}} = 2.83
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A z-score of 2.83 is 0.9977.  This means there is a 0.9977 probability the mean height will be below 72 inches.
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Probability the mean height is less than 70 inches:
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z2 = {{{(70-71)/(1/sqrt(8))}}} = -2.83
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A z-score of -2.83 is 0.0023.  This means there is a 0.0023 probability the mean height will be below 70 inches.
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To find the probability the mean height will be between 70 and 72 inches, simply subtract these two probabilities from one another:
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0.9977 - 0.0023 = 0.9954
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<b>There is a 0.9954 probability the mean height will be between 70 and 72 inches.</b>