Example 2 Assume that the weights of all packages of a certain brand of cookies are normally distributed with a mean of 32 ounces and a standard deviation of 0.3 ounce. Find the probability that the mean weight * of a random sample of 20 packages of this brand of cookies will be between 31.8 and 31.9 ounces. [0.0667] Example 3 According to Sallie Mae surveys and Credit Bureau data, college students carried an average of $3173 credit card debt in 2008. Suppose the probability distribution of the current credit card debts of all college students in United States is unknown but its mean is $3173 and the standard deviation is $750. Let * be the mean credit card debt of a random sample of 400 U.S. college students. (a) What is the probability that the mean of the current credit card debts for this sample is within $70 of the population mean? [0.9381] (b) What is the probability that the mean of the current credit card debts for this sample is lower than the population mean by $50 or more? [0.09121]