The average number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds (Source: American Dietetic Association). If a sample of 50 individuals is randomly selected, find the
Probability that the mean of the sample will be greater than 200 pounds.
A)0.0985
B)0.7613
C)0.8815
D)0.9015

Question

Quizplus · Accepted Answer

To find the probability that the mean of the sample will be greater than 200 pounds, we use the formula for the standard error of the mean: SE = σ / √n, where σ is the standard deviation and n is the sample size. Here, σ = 22 pounds and n = 50. So, SE = 22 / √50 = 3.11. We then find the z-score for 200 pounds: z = (X - μ) / SE = (200 - 196) / 3.11 = 1.29. Using the z-table, we find the probability corresponding to z = 1.29, which is approximately 0.9015. However, since we want the probability that the mean is greater than 200 pounds, we subtract this value from 1, giving 1 - 0.9015 = 0.0985.

The Average Number of Pounds of Red Meat a Person