olivia asked in Science & MathematicsMathematics · 6 months ago

Statistics Help?

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.36 and a standard deviation of 1.46. Using the empirical rule, what percentage of American women have shoe sizes that are at least 11.28? Please do not round your answer.

Relevance
• 6 months ago

You need to find the z-score, which can be found with:

n = m + sz

where:

n = the data point you are looking for (11.28)

m = the mean (8.36)

s = the standard deviation (1.46)

z = the z-score (unknown)

Substitute what we know and solve:

n = m + sz

11.28 = 8.36 + 1.46z

2.92 = 1.46z

2 = z

The empirical rule states that 95% of data points are within 2 standard deviations from the mean. This would include the range of:

-2s < m < 2s

You are asked for "at least 11.28" which means you don't want the range above, but the upper portion of what's left.

So if we don't want the range from -2s < m < 2s, we look at the negative data points:

x < -2s and x > 2s

which takes up 5% of the data.

But since we only want the values above 2s, not below -2s, we throw out that half, which leaves us with:

2.5% of the data points being larger than 11.28 for a shoe size.

• Mike G
Lv 7
6 months ago

z(x=11.28) = (11.28-8.36)/1.46 = 2

95/2 = 47.5

100-50-47.5 = 2.5