The amount of time it takes to complete an examination has a skewed-left distribution with a mean of 65 minutes and a standard deviation of 8 minutes. If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal for large sample sizes. Given the mean of 65 minutes and a standard deviation of 8 minutes, the standard error for the sample mean of 64 students is 1 minute. A sample mean of 71 minutes is 6 standard deviations above the mean, making it extremely unlikely, hence the probability is approximately 0.

The Amount of Time It Takes to Complete an Examination