The number of hours spent studying by students on alarge campus in the week before final exams followsa normal distribution with a standard deviation of8.4 hours. a random sample of these students is takento estimate the population mean number of hoursstudying. a. how large a sample is needed to ensure that theprobability that the sample mean differs from thepopulation mean by more than 2.0 hours is lessthan 0.05? b. without doing the calculations, state whether alarger or smaller sample size compared to the sam-ple size in part (a) would be required to guaranteethat the probability of the sample mean differingfrom the population mean by more than 2.0 hoursis less than 0.10.c. without doing the calculations, state whether alarger or smaller sample size compared to the sam-ple size in part (a) would be required to guaranteethat the probability of the sample mean differingfrom the population mean by more than 1.5 hours isless than 0.05.