Use technology to solve the following problem: A survey reported that in a recent year, the mean serum cholesterol level in milligrams per deciliter for U.S. adults was 195 with a standard deviation Of 35. A random sample of 110 adults was chosen. Find the 77th percentile of the sample mean.
A) 197.6
B) 220.9
C) 197.5
D) 195.2

Question

Quizplus · Accepted Answer

To find the 77th percentile of the sample mean, we need to use the standard normal distribution since the sample size is greater than 30 (central limit theorem).

First, we need to find the standard error of the mean:
standard error of the mean = standard deviation / √sample size
standard error of the mean = 35 / √110
standard error of the mean ≈ 3.34

Next, we need to find the z-score associated with the 77th percentile:
z-score = invNorm(0.77)
z-score ≈ 0.61

Finally, we can use the formula for the standard normal distribution:
z = (x̄ - μ) / (σ/√n)
0.61 = (x̄ - 195) / (35/√110)

Solving for x̄ gives us:
x̄ ≈ 197.5

Therefore, the 77th percentile of the sample mean is approximately 197.5. The best choice is C.

Use Technology to Solve the Following Problem: a Survey Reported