Question

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.438.43 and a standard deviation of 1.51.5. Using the empirical rule, what percentage of American women have shoe sizes that are between 6.936.93 and 9.939.93

Answer 1

Answer:

The right solution is "68%".

Step-by-step explanation:

The empirical rule is:

$X\sim N(8.43, 1.5)$

According to the question,

= $P(6.93< \mu < 9.93)$

= $P(\frac{6.93-8.43}{1.5} < \frac{\mu -8.43}{1.5} < \frac{9.93-8.43}{1.5} )$

= $P(z(1)-P(z(-1))$

= $68$ (%)

Thus the above is the right solution.