Question

Women’s heights are approximately normally distributed with mean = 64

inches and standard deviation = 4 inches. What is the probability that a
randomly selected woman is between 66 and 73 inches tall?

Answer 1

To find the probability that a randomly selected woman is between 66 and 73 inches tall, we use the standard normal distribution and convert the heights to z-scores. The probability is approximately 0.4882.

Step-by-step explanation:

To find the probability that a randomly selected woman is between 66 and 73 inches tall, we can use the standard normal distribution and convert the heights to z-scores.

To find the z-score for 66 inches, we use the formula z = (x - μ) / σ, where x is the height, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (66 - 64) / 4 = 0.5.

Similarly, for 73 inches, we find z = (73 - 64) / 4 = 2.25.

Using a standard normal distribution table or a calculator, we can find the area under the curve between these two z-scores, which represents the probability. The probability that a randomly selected woman is between 66 and 73 inches tall is approximately 0.4882.