Question

According to a human modeling​ project, the distribution of foot lengths of women is approximately Normal with a mean of 23.4 centimeters and a standard deviation of 1.3 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?

Answer 1

Answer: 22.0.6%

Step-by-step explanation:

Given : According to a human modeling​ project, the distribution of foot lengths of women is approximately Normal with $\mu=23.3\ cm$ and $\sigma=1.3\ cm$.

In the United​ States, a​ woman's shoe size of 6 fits feet that are 22.4 centimeters long.

Then, the probability that women in the United States will wear a size 6 or​ smaller :-

$P(x\leq22.4)=P(z\leq\dfrac{22.4-23.4}{1.3})\ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\\approx P(z\leq-0.77)\\\\=1-P(z\leq0.77)\\\\=1-0.77935=0.2206499\approx0.2206=22.06\%$

Hence,  the required answer = 22.0.6%