Question

suppose the mean of a normally distributed population is 300, and 200 simple random samples are drawn from the population. at a 68% confidence level (one standard deviation from the mean), about how many of the samples’ confidence intervals would you expect to contain the population mean?
options: 64, 96, 136, 204

Explanation:

Step1: Understand Confidence Level

A 68% confidence level (one standard deviation from the mean in a normal distribution) means that we expect about 68% of the confidence intervals from random samples to contain the population mean.

Step2: Calculate Number of Intervals

We have 200 samples. To find the number of intervals that contain the mean, we calculate 68% of 200.
First, convert 68% to a decimal: \( 68\% = 0.68 \)
Then multiply by the number of samples: \( 0.68 \times 200 = 136 \)

Answer:

136 (corresponding to the option with 136, likely the third option if options are ordered as 64, 96, 136, 204)