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A sport statistician gathered data on the number of points scored in each game by high school basketball players across the country. She found a population mean of 20.15 and a standard deviation of 3.7. Each sample size was 20 players. By the central limit theorem, which interval do 68% of the sample means fall within?

A.
19.96 and 20.34
B.
18.50 and 21.81
C.
17.67 and 22.63
D.
19.32 and 20.98

Respuesta :

raphealnwobi

For a sample size of 20 players, 68% of the sample means fall within 19.32 and 20.98

What is empirical rule?

Empirical rule states that for a normal distribution, 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean.

For a population mean of 20.15 and a standard deviation of 3.7:

68% are within μ ± σ/√n, hence:

68% = 20.15 ± 3.7/√20 = (19.32, 20.98)

For a sample size of 20 players, 68% of the sample means fall within 19.32 and 20.98

Find out more empirical rule at: https://brainly.com/question/10093236

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