Question

College Graduate-Level Wages. The Economic Policy Institute periodically issues reports on worker's wages. The institute reported that mean wages for male college graduates were $37.59 per hour and for female college graduates were $27.83 per hour in 2017. Assume the standard deviation for male graduates is $4.60, and for female graduates it is $4.10. a. What is the probability that a sample of 50 male graduates will provide a sample mean within $1.00 of the population mean, $37.39?

Answer 1

To calculate the probability that a sample of 50 male graduates will have a sample mean within $1.00 of the mean, we use the Central Limit Theorem and calculate the standard error. We then find the Z-scores for $1.00 above and below the mean and look up the corresponding probabilities in the standard normal distribution table, finally adding these probabilities to find the total probability.

Step-by-step explanation:

The question asks about the probability that a sample of 50 male graduates will have a sample mean within $1.00 of the population mean ($37.59) given a standard deviation of $4.60. To find this, we can use the Central Limit Theorem which states that for a sufficiently large sample size, the distribution of the sample mean will approximate a normal distribution even if the population distribution is not normal.

First, we calculate the standard error (SE) of the mean using the formula SE = σ / √(n), where σ is the standard deviation and n is the sample size. This gives us SE = $4.60 / √(50). Then we find the Z-scores for $1.00 above and below the population mean and use the standard normal distribution table to find the probability that the sample mean is within those Z-scores.

For example:

• Calculate the standard error: SE = $4.60 / √(50) ≈ $0.6504
• Calculate the Z-score for $37.59 + $1.00 and $37.59 - $1.00
• Use the Z-scores to find the corresponding probabilities in the standard normal distribution table
• Add the probabilities of the Z-scores to find the total probability