Question

A bicycle company is designing women's bicycle frames The frames can accommodate any woman taller than 54.5 inches. Given that the heights of adult American women are normally distributed, with a mean of 65 inches and a standard deviation of 3.5 inches, what percentage of American women CANNOT use the bicycles designed by this company?​

Answer 1

Using the normal distribution, it is found that 0.13% of American women CANNOT use the bicycles designed by this company.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

$\mu = 65, \sigma = 3.5$

The proportion of women that cannot use the bikes(smaller than 54.5 inches) is the p-value of Z when X = 54.5, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{54.5 - 65}{3.5}$

Z = -3

Z = -3 has a p-value of 0.0013.

0.0013 = 0.13% of American women CANNOT use the bicycles designed by this company.

More can be learned about the normal distribution at brainly.com/question/27850813

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