According to a human modeling project, the distribution of foot lengths of women is approximately Normal with a mean of 23.3 centimeters and a standard deviation of 1.4 centimeters. In the United States, a woman's shoe size of 6 fits feet that are 22.4 centimeters long. What percentage of women in the United States will wear a size 6 or smaller?

26.11% of women in the United States will wear a size 6 or smaller

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

In the United States, a woman's shoe size of 6 fits feet that are 22.4 centimeters long. What percentage of women in the United States will wear a size 6 or smaller?

This is the pvalue of Z when X = 22.4. So

has a pvalue of 0.2611

26.11% of women in the United States will wear a size 6 or smaller

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