3. A random sample of 49 four-year public colleges has a mean annual tuition of $5,900. Suppose annual tuition at four-year public colleges is distributed normally with a known standard deviation (o ) of $689. (Note: selected z* values from Table C are listed at the top of this exam.) (a) (5 pts.) Construct a 99% confidence interval for the average tuition at four-year public colleges, rounded to the nearest dollar. (b) (5 pts.) Interpret the interval in part (a) above (i.e. say in words what it means). (c) (5 pts.) How many four-year public colleges must we sample if we want to estimate mean annual tuition at four-year public colleges within a margin of error of + $210 with 99% confidence? (d). (4 pt.) What would be the critical value (z*) if the confidence level was changed to 92%