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) 0.5734
B) 0.5707
C) 0.8547
D) 0.9522
E) 0.4257

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. ​
A) ​0.5734
B) ​0.5707
C) ​0.8547
D) ​0.9522
E) ​0.4257

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