Question

The amount of time it takes an Intro to Statistics instructor to grade an individual test is a random variable with expected value 3 minutes and standard deviation 1 minute. She has 64 tests to grade and begins grading at 7:40 PM. What is the probability that she is finished grading by the beginning of the 11:00 PM news?

Answer 1

The probability that the instructor is finished grading by the beginning of the 11:00 PM news is 99.92%.

Step-by-step explanation:

To find the probability that the instructor is finished grading by the beginning of the 11:00 PM news, we need to calculate the Z-score and use the standard normal distribution table.

First, let's find the Z-score: Z = (11:00 PM - 7:40 PM - 64*3 minutes) / (64 minutes * 1 minute) = (660 minutes - 460 minutes) / 64 minutes = 200 / 64 = 3.125

Using the standard normal distribution table, we can find the probability corresponding to a Z-score of 3.125. The probability is approximately 0.9992. Therefore, the probability that the instructor is finished grading by the beginning of the 11:00 PM news is 0.9992 or 99.92%.

Answer 2

To calculate the probability that the instructor is finished grading by the beginning of the 11:00 PM news, find the z-score corresponding to the remaining time and use the standard normal distribution table to find the probability.

Step-by-step explanation:

To calculate the probability that the instructor is finished grading by the beginning of the 11:00 PM news, we need to find the probability that grading 64 tests takes less than or equal to the time remaining from 7:40 PM to 11:00 PM.

Since grading an individual test is a random variable with an expected value of 3 minutes and a standard deviation of 1 minute, we can approximate the grading time as a normally distributed random variable.

We need to find the z-score corresponding to the remaining time and use the z-score to find the probability from the standard normal distribution table.

Once we have the probability, we can subtract it from 1 to find the probability that the instructor is finished grading by the beginning of the 11:00 PM news.