Question

historically, heights of women have a bell - shaped disribution with a mean of 158.5 and a standard deviation of 6.4. use the empirical rule to approximate the percentage of heights of women between 145.7cm and 171.3cm. select an answer

Explanation:

Step1: Calculate z - scores

For $x_1 = 145.7$, $z_1=\frac{145.7 - 158.5}{6.4}=\frac{- 12.8}{6.4}=-2$.
For $x_2 = 171.3$, $z_2=\frac{171.3 - 158.5}{6.4}=\frac{12.8}{6.4}=2$.

Step2: Apply Empirical Rule

The Empirical Rule states that for a bell - shaped (normal) distribution, about 95% of the data lies within $z=-2$ and $z = 2$.

Answer:

95%