Question

According to a human modeling​ project, the distribution of foot lengths of women is approximately normal with a mean of centimeters and a standard deviation of centimeters. In the united​ states, a​ woman's shoe size of fits feet that are centimeters long. What percentage of women in the united states will wear a size or​ smaller?.

Answer 1

The percentage of women in the united states will wear a size 6 fits or​ smaller is 22.07%.

Z score

The z score is used to determine by how many standard deviations, the raw score is above or below the mean. It is given by:

z = (x - μ)/σ

where x is raw score, μ is mean and σ is standard deviation.

μ = 23.4, σ = 1.3, x = 6 fits = 22.4, hence:

For x < 22.4:

z = (22.4 - 23.4)/1.3 = -0.77

P(z < -0.77) = 0.2207

The percentage of women in the united states will wear a size 6 fits or​ smaller is 22.07%.

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