QuestionAugust 25, 2025

Women's shoe sizes can be modeled by a normal distribution. In the United States, the mean women's shoe size is 8, with a standard deviation of 1.5 What is the probability that a randomly selected woman in the United States has a shoe size greater than 125? square (enter an exact decimal) POSSIBLE POINTS: 7.69

Women's shoe sizes can be modeled by a normal distribution. In the United States, the mean women's shoe size is 8, with a standard deviation of 1.5 What is the probability that a randomly selected woman in the United States has a shoe size greater than 125? square (enter an exact decimal) POSSIBLE POINTS: 7.69
Women's shoe sizes can be modeled by a normal distribution. In the United States, the mean women's shoe size is 8, with a standard deviation of 1.5 What is the probability that a randomly selected woman in the United States has a shoe size greater than 125? square (enter an exact decimal) POSSIBLE POINTS: 7.69

Solution
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Answer

0 Explanation 1. Identify the problem Determine if the shoe size of 125 is within a reasonable range for the given distribution. 2. Analyze the distribution The mean is 8, and the standard deviation is 1.5. A shoe size of 125 is extremely far from the mean. 3. Calculate Z-score **Z = \frac{X - \mu}{\sigma}** where ( X = 125 ), ( \mu = 8 ), ( \sigma = 1.5 ). \( Z = \frac{125 - 8}{1.5} = \frac{117}{1.5} = 78 \). 4. Interpret the Z-score A Z-score of 78 is extraordinarily high, indicating an almost zero probability in a normal distribution.

Explanation

1. Identify the problem<br /> Determine if the shoe size of 125 is within a reasonable range for the given distribution.<br />2. Analyze the distribution<br /> The mean is 8, and the standard deviation is 1.5. A shoe size of 125 is extremely far from the mean.<br />3. Calculate Z-score<br /> **Z = \frac{X - \mu}{\sigma}** where ( X = 125 ), ( \mu = 8 ), ( \sigma = 1.5 ).<br /> \( Z = \frac{125 - 8}{1.5} = \frac{117}{1.5} = 78 \).<br />4. Interpret the Z-score<br /> A Z-score of 78 is extraordinarily high, indicating an almost zero probability in a normal distribution.
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