Question

Assume college women have heights with the following distribution (inches): N(68, 1.1). Find the height at the 75th percentile. The 75th percentile is 8.71. Round to one decimal place as needed.)

Answer 1

To find the height at the 75th percentile in a normal distribution, we use the z-score formula. By substituting the given values into the formula, we find that the height at the 75th percentile is approximately 68.74 inches.

Step-by-step explanation:

To find the height at the 75th percentile, we will use the concept of the standard normal distribution. Since we are given the mean (68) and the standard deviation (1.1), we can calculate the z-score corresponding to the 75th percentile. The formula for the z-score is:

z = (x - μ) / σ

By substituting the given values, we get:

z = (x - 68) / 1.1

To find the height (x) at the 75th percentile, we need to find the z-score that corresponds to a cumulative probability of 0.75. Consulting a standard normal distribution table or using a calculator, we find that the z-score is approximately 0.674. Substituting this value into the formula gives:

0.674 = (x - 68) / 1.1

Now we can solve for x:

x = 0.674 * 1.1 + 68

Calculating this, we get:

x ≈ 68.74