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?
Accepted Solution
A:
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 [tex]\mu=23.3\ cm[/tex] and [tex]\sigma=1.3\ cm[/tex].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 :-[tex]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\%[/tex]Hence, the required answer = 22.0.6%