Question

The weight of National Football League (NFL) players has increased steadily, gaining up to 1.5 lb. per year since 1942. According to ESPN, the average weight of a NFL player is now 245.86 lb. Assume the population standard deviation is 20 lb.

If a random sample of 50 players is selected, what is the probability that the sample mean will be less than 250 lb.?

Answer 1

To find the probability that the sample mean will be less than 250 lb., we need to calculate the z-score and find the corresponding probability using the z-table or a statistical calculator.

Step-by-step explanation:

To solve this problem, we need to calculate the z-score for the sample mean. The formula for calculating the z-score is:

z = (x - μ) / (σ / sqrt(n))

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, the sample mean is 250 lb., the population mean is 245.86 lb., the population standard deviation is 20 lb., and the sample size is 50.

Substituting these values into the formula, we get:

z = (250 - 245.86) / (20 / sqrt(50))

z = 4.14 / (20 / 7.07)

z = 0.7316

Next, we need to find the probability corresponding to this z-score using the z-table or a statistical calculator.