Question

A probability distribution has a mean of 50 and a standard deviation of 15. We plan to take a sample of 35 observations. What is the probability that the sample mean is between 53 and 54?

(Select one).
a. 0.0619
b. 0.4971
c. 0.1554
d. 0.8239

Answer 1

To find the probability that the sample mean is between 53 and 54, we need to calculate the z-scores and find the area under the standard normal curve. The probability is approximately a) 0.0619.

Step-by-step explanation:

To find the probability that the sample mean is between 53 and 54, we need to calculate the z-scores for 53 and 54 using the formula:

z = (x - μ) / (σ / √n)

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

Using the given information, we have:

z1 = (53 - 50) / (15 / √35) ≈ 1.94

z2 = (54 - 50) / (15 / √35) ≈ 2.19

Next, we find the area under the standard normal curve between these two z-scores using a standard normal distribution table or a calculator. The probability is the difference between the two areas which is approximately 0.0619.

Therefore, the correct answer is a. 0.0619.