The Illinois Student Senate wants to know the mean amount of money spent by Illinois students for textbooks this semester. Suppose the population mean based on past data over the past few years is $450 and the population standard deviation is $40. A random sample of 625 students is taken.

(a) What is the probability that the sample mean will be less than $452?

(b) What is the probability that the sample mean will be within $2 of $450? That is, what is the probability that the sample mean will be between $448 and $452?

(c) What is the probability that the sample mean will be within $10 of $450? That is, what is the probability that the sample mean will be between $440 and $460?