Question

Researchers have found that the number of steps the average American takes is normally distributed. The mean of the number of steps is 4500 and the standard deviation is 600. Between what 2 numbers do 95% of all American fall?

A. 3300 to 5700
B. 2700 to 6300
C. 3900 to 5100
D. 4000 to 5000

Answer 1

95% of all Americans' step counts fall within 3300 and 5700 steps according to the empirical rule, which states that about 95% of data in a normal distribution falls within two standard deviations of the mean, using a mean of 4500 and a standard deviation of 600.

Step-by-step explanation:

To find the range within which 95% of all Americans' step counts fall, given the mean μ (mu) is 4500 steps and the standard deviation σ (sigma) is 600 steps, we use the empirical rule. The empirical rule states that approximately 95% of the data in a normal distribution falls within two standard deviations of the mean.

Calculating the range:

Subtract two standard deviations from the mean: 4500 - (2 × 600) = 3300.Add two standard deviations to the mean: 4500 + (2 × 600) = 5700.

Therefore, 95% of all Americans' step counts fall between 3300 and 5700 steps. The correct answer is A. 3300 to 5700.