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.

Question

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. ​

Quizplus · Accepted Answer

First, we need to convert the heights given in the problem 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 given mean and standard deviation:

z1 = (64 - 64.5) / 2.7 = -0.1852
 z2 = (72 - 64.5) / 2.7 = 2.7778

Now, we can use the standard normal distribution to find the area between these two z-scores. Using a symbolic integration utility, we can find:

P(-0.1852 < Z < 2.7778) ≈ 0.5707

Therefore, the answer is B.

Suppose the Mean Height of American Women Between the Ages