Respuesta :
Answer:
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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:
[tex]\mu = 23.3, \sigma = 1.4[/tex]
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
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22.4 - 23.3}{1.4}[/tex]
[tex]Z = -0.64[/tex]
[tex]Z = -0.64[/tex] has a pvalue of 0.2611
26.11% of women in the United States will wear a size 6 or smaller
