Final answer:
The question pertains to calculating probabilities of sample means being within a particular range of the population mean, which involves the use of z-scores and the standard normal distribution. Without specific standard deviations and means, numerical probabilities cannot be computed. However, larger sample sizes typically result in higher probabilities of sample means being closer to the population mean.
Step-by-step explanation:
The question relates to the probability of sample means being within a certain range of the population mean. To find this probability for sample sizes and specified deviations from the mean, we would use the Central Limit Theorem and calculate z-scores to compare with the standard normal distribution. Specific sample standard deviations and population means aren't provided in the original question, so a generic approach to solving these problems would involve assuming the population standard deviation or estimating it with the sample standard deviation, then using the formula for the standard error (SE = σ/√n, where σ is the standard deviation and n is the sample size), and applying the z-score formula (z = (X - μ)/SE, where X is the sample mean, μ is the population mean). Due to the lack of numerical data in the question, we cannot numerically calculate these probabilities. However, the larger the sample size, the closer the sample means will tend to be to the population mean, according to the Law of Large Numbers.
Regarding the comparison of probabilities between male and female graduates, without additional data on the variance of their earnings, it is not possible to definitively say which group would have a higher probability of the sample mean being within $0.50 of the population mean. Generally, if the variances were the same, a larger sample size would typically give a higher probability of the sample mean being closer to the population mean. For part (d), again, without the standard deviation of the female graduates' earnings, the probability cannot be calculated.