Question

A sample of 9 people has a mean of 200 and a standard deviation of 10. What is the probability that their sample mean will be larger than 207.7?

a) 0.0057
b) 0.0228
c) 0.9943
d) 0.9772

Answer 1

Using the Z-score formula and standard normal distribution, the probability of the sample mean being greater than 207.7 with the given mean and standard deviation is 0.0228.

Step-by-step explanation:

The question asks about the probability that the sample mean of a group will be larger than a particular value given the sample mean and standard deviation. To solve this, you can use the Z-score formula which is Z = (X - μ) / (σ / √n), where X is the value in question, μ is the mean, σ is the standard deviation, and n is the sample size.

To find the probability of the sample mean being greater than 207.7 when n=9, μ=200, and σ=10, first calculate the Z-score.

Z = (207.7 - 200) / (10 / √9) = 7.7 / (10 / 3) = 7.7 / 3.333 = 2.31

Once you have the Z-score, you would look up this value on a standard normal distribution table or use a calculator with Z-score functionality to find the probability.

The probability that the sample mean will be larger than 207.7 is the area to the right of the Z-score, which corresponds to option b) 0.0228.