Respuesta :
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%
If the distribution of foot lengths of women is approximately Normal with a mean of 23.4 centimetre and a standard deviation of 1.3 centimetre and a woman's shoe size of 6 fits feet that are 22.4 centimetre long. then percentage of women in the United States will wear a size 6 or smaller is 22.06%
What is probability ?
Probability is chances of occurring of an event.
Given that
the distribution of foot lengths of women is approximately Normal with a mean of 23.4 centimetre and a standard deviation of 1.3 centimetre.
And it's also given that
a woman's shoe size of 6 fits feet that are 22.4 centimetre long.
The probability that women in the United States will wear a size 6 or smaller can be calculated as
[tex]P(x \leq 22.4)=P\left(z \leq \frac{22.4-23.4}{1.3}\right) \\\\$\approx P(z \leq-0.77)$\\\\$=1-P(z \leq 0.77)$\\$=1-0.77935=0.2206499 \\\\\approx 0.2206$[/tex]
=22.06 %
If the distribution of foot lengths of women is approximately Normal with a mean of 23.4 centimetre and a standard deviation of 1.3 centimetre and a woman's shoe size of 6 fits feet that are 22.4 centimetre long. then percentage of women in the United States will wear a size 6 or smaller is 22.06%
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