Suppose that adult women in China have heights that are normally distributed with a mean = 155 centimeters and a standard deviation = 8 centimeters. Adult women in Japan have heights which are normally distributed with a mean = 158 cm and a standard deviation = 6 cm. Of the Chinese women, what percent are shorter than 163cm?

84.134%

Step-by-step explanation:

We solve this question using the z score formula.

The formula for calculating a z-score is z = (x-μ)/σ

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

We are were asked in the question that:

Suppose that adult women in China have heights that are normally distributed with a

mean = 155 centimeters

standard deviation = 8 centimeters. Of the Chinese women, what percent are shorter than 163cm?

Using the z score formula

z = (x-μ)/σ

z = (163 - 155)/8

z = 8/8

z = 1

Determining the Probability value from Z-Table:

P(x ≤ 163) = P(x < 163)

= 0.84134

Converting to percentage

= 0.84134 × 100%

= 84.134%

The percent of Chinese women that are shorter than 163cm is 84.134%