Final answer:
To find the standard error and Z value for the amount spent on books by university students, one must apply the appropriate formulas using the provided standard deviation, sample size, and the expenditure amount in question. The probability for spending less than a given amount is found by using the Z value with a standard normal distribution.
Step-by-step explanation:
To calculate the standard error for the money spent on books in the sample, we use the formula for the standard error of the mean (SEM), which is the standard deviation divided by the square root of the sample size (n): SEM = \( \frac{\sigma}{\sqrt{n}} \). Given a standard deviation (\( \sigma \)) of $248 and a sample size (n) of 71 students, the calculation would be SEM = \( \frac{248}{\sqrt{71}} \), rounded to one decimal place.
To find the Z value for $483 spent on books in the sample, we use the formula Z = \( \frac{X - \mu}{SEM} \), where X is $483, and \( \mu \) is the mean expenditure of $518. The probability of a sample having an average amount spent on books of less than $483 can then be determined by looking up this Z value in a standard normal distribution table, or using a statistical software.