Question

The mean height of women in a country (ages 20−29 ) is 64.4 inches. A random sample of 55 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume σ=2.87.

Answer 1

To find the probability that the mean height for the sample is greater than 65 inches, use the z-score formula and a z-table or calculator.

Step-by-step explanation:

To find the probability that the mean height for the sample is greater than 65 inches, we need to use the z-score formula. The formula is:

z = (x - μ) / (σ / √n)

Given that the mean height of women is 64.4 inches, the standard deviation is 2.87 inches, and the sample size is 55, we can plug these values into the formula as follows:

z = (65 - 64.4) / (2.87 / √55) = 0.6 / (2.87 / 7.416) = 0.6 / 0.387 = 1.55

Using a z-table or a calculator, we can find that the probability of a z-score greater than 1.55 is approximately 0.0606, or 6.06%.