Question

Assume that women's heights are normally distributed with a mean given by u = 62.3 in, and a standard deviation given by c = 2.6 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 63 in. (b) If 48 women are randomly selected, find the probability that they have a mean height less than 63 in. (a) The probability is approximately ) (Round to four decimal places as needed.)

Answer 1

To find the probability that a randomly selected woman's height is less than 63 inches, calculate the z-score and use the standard normal distribution table.

Step-by-step explanation:

To find the probability that a randomly selected woman's height is less than 63 inches, we need to calculate the z-score and use the standard normal distribution table.

First, calculate the z-score using the formula: z = (x - u) / c, where x is the given value (63 inches), u is the mean (62.3 inches), and c is the standard deviation (2.6 inches).

Plugging in the values, we get: z = (63 - 62.3) / 2.6 = 0.2692.

Next, we can use the standard normal distribution table or a calculator to find the probability associated with the z-score. The probability that a randomly selected woman's height is less than 63 inches is approximately 0.6059.