Question

After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,100. If a sample of 100 students is selected, what is the probability that the sample mean cost to attend USC is greater than $26,500?

Answer 1

To find the probability that the sample mean cost to attend USC is greater than $26,500, we need to calculate the z-score and use the standard normal distribution.

Step-by-step explanation:

To find the probability that the sample mean cost to attend USC is greater than $26,500, we need to calculate the z-score and use the standard normal distribution.

1. Calculate the z-score using the formula: z = (sample mean - population mean) / (population standard deviation / √sample size).
2. Find the area under the standard normal curve to the right of the z-score using a z-table or calculator.
3. The probability that the sample mean cost to attend USC is greater than $26,500 is equal to 1 minus the probability found in step 2.

Let's calculate it step by step:

1. Calculate the z-score: z = ($26,500 - $27,100) / ($27,100 / √100) = -2.216.
2. Find the area to the right of the z-score: P(z > -2.216) = 1 - P(z < -2.216). Using a z-table or calculator, we find that P(z < -2.216) = 0.0136.
3. The probability that the sample mean cost to attend USC is greater than $26,500 is 1 - 0.0136 = 0.9864, or 98.64%.