Use technology to solve the following problem: The mean number of pets per household is 3.03 with standard deviation 1.5. A sample of 56 households is drawn. Find the 62nd percentile of the Sample mean.
A) 3.95
B) 2.57
C) 3.09
D) 3.65

Question

Quizplus · Accepted Answer

To find the 62nd percentile of the sample mean, we need to use the formula for the z-score of a sample mean:

z = (x̄ - μ) / (σ / √n)

where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. We want to find the value of x̄ that corresponds to the 62nd percentile, which is equivalent to finding the z-score that corresponds to the 62nd percentile.

From standard normal distribution tables, we know that the z-score corresponding to the 62nd percentile is approximately 0.36.

Plugging in the values we know:

0.36 = (x̄ - 3.03) / (1.5 / √56)

Solving for x̄:

x̄ = 3.09

Therefore, the 62nd percentile of the sample mean is approximately 3.09. The best choice is C.

Use Technology to Solve the Following Problem: the Mean Number