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 less than 200 pounds.
A)0.9015
B)0.0985
C)0.7613
D)0.8815

Question

Quizplus · Accepted Answer

To find the probability that the mean of the sample will be less than 200 pounds, we use the formula for the standard error of the mean: $SE = \frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the standard deviation and $n$ is the sample size. Here, $\sigma = 22$ pounds and $n = 50$, so $SE = \frac{22}{\sqrt{50}} \approx 3.11$. We then calculate the z-score for a sample mean of 200 pounds: $z = \frac{\bar{x} - \mu}{SE} = \frac{200 - 196}{3.11} \approx 1.29$. Looking up 1.29 in the z-table gives us the probability of 0.9015 that the sample mean will be less than 200 pounds.

The Average Number of Pounds of Red Meat a Person