Question

The average credit card debt for college seniors is $22,199 with a standard deviation of $5300. What is the probability that a sample of 30 seniors owes a mean of more than $20,200? Round answer to 4 decimal places. Answer:

Answer 1

The probability that a sample of 30 college seniors owes a mean of more than $20,200 is 1 (or 100%).

Step-by-step explanation:

To find the probability that a sample of 30 college seniors owes a mean of more than $20,200, we can use the Central Limit Theorem and the Z-score formula.

First, let's calculate the Z-score:

Z = (X - μ) / (σ / √n)

where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values:

Z = (20200 - 22199) / (5300 / √30)

Z = -4.630

Using a Z-table or a calculator, we can find that the probability of a Z-score less than -4.630 is approximately 0.00000.

Since we want the probability of a mean more than $20,200, which corresponds to a Z-score less than -4.630, we can subtract the probability from 1:

Probability = 1 - 0.00000 = 1

Therefore, the probability that a sample of 30 college seniors owes a mean of more than $20,200 is 1 (or 100%).