Question

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.1 and a standard deviation of 1.47. Using the empirical rule, what percentage of American women have shoe sizes that are greater than 5.16?

Answer 1

97.5% of American women have shoe sizes that are no more than 11.47.

Lets try to solve the question,

Given values ,

Dev (u) = 8.47

Standard deviation (x) = 1.47

So we e have to find the percentage of American women whose shoe size's are not more than 11.47 P(x<11.47).

Lets find z score by using empirical formula.

=> $z= (x-u) / a$

=> $11.47-8.47/1.5$

=> $z= 2$

Now we have to find $P(z < 2)$ . Using the empirical rule, we know that 97.5% data lies below 2 standard deviations above mean.

Therefore the 97.5% of American women have shoe sizes that are no more than 11.47.

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