Question

a large data sample of heights of US women is normally distributed with a mean height of 64.2 inches and a standard deviation of 2.6 inches. What is the approximate probability that a randomly selected person in this sample is shorter than 61.6 inches? (I need this by Tuesday the 22nd)

Answer 1

To find the probability that a randomly selected person is shorter than 61.6 inches, calculate the z-score and use a standard normal distribution table or calculator to find the corresponding probability.

Step-by-step explanation:

To find the approximate probability that a randomly selected person in the sample is shorter than 61.6 inches, we can use the standard normal distribution.

First, we need to calculate the z-score for 61.6 inches using the formula:
z = (x - mean) / standard deviation

z = (61.6 - 64.2) / 2.6 = -1.0

We can then use a standard normal distribution table or a calculator to find the area to the left of z = -1.0, which represents the probability that a randomly selected person is shorter than 61.6 inches. The probability is approximately 0.1587, or 15.87%.