Suppose the mean height of American women between the ages of 30 and 39 is 64.5 inches, and the standard deviation is 2.7 inches. Use a symbolic integration utility to approximate the probability that a 30-to 39-year-old woman chosen at random is between 5 feet 4 inches and 6 feet tall.
A)0.8547
B)0.5707
C)0.4257
D)0.5734
E)0.9522

Question

Quizplus · Accepted Answer

First, we need to convert the heights to inches. 5 feet 4 inches is equal to 64 inches, and 6 feet is equal to 72 inches.

Next, we need to standardize these values using the formula z = (x - µ) / σ, where x is the height, µ is the mean height, and σ is the standard deviation.

For 64 inches, z = (64 - 64.5) / 2.7 ≈ -0.1852
For 72 inches, z = (72 - 64.5) / 2.7 ≈ 2.7778

We want to find the probability that a woman's height is between these two z-scores. We can find this by taking the difference between the cumulative probabilities at these two z-scores. Using a symbolic integration tool, we can find that:

P(-0.1852 < z < 2.7778) ≈ 0.5707

Therefore, the best choice is B.

Suppose the Mean Height of American Women Between the Ages