2. Students studying at SAIS DC spend an average of $172.50 per week on basic needs other than housing. Use this gure as the population mean and assume that population standard deviation is $70.00. a) What is the probability that the mean expenditure for a sample of 35 students is within $20 of the population mean? What assumption do you need to make for this calculation? b) What is the probability that the mean expenditure for a sample of 70 students is within $20 of the population mean? c) Which, if any, of the sample sizes in parts (a) and (b), would you recommend jl_'!_g[_c_l_r__l_:g have at least a .95 probability that the sample mean is within $20 of the population mean