5.14 sat scores: sat scores of students at an ivy league college are distributed with a standard deviation of 250 points. two statistics students, raina and luke, want to estimate the average sat score of students at this college as part of a class project. they want their margin of error to be no more than 25 points. (a) raina wants to use a 90% con dence interval. how large a sample should she collect? raina should sample at least people. (b) luke wants to use a 99% con dence interval. without calculating the actual sample size, determine whether his sample should be larger or smaller than raina's, and explain your reasoning. larger higher degrees of confidence require larger margins of error smaller because higher degrees of confidence require smaller margins of error smaller since luke has a higher level of confidence in his results than raina (c) calculate the minimum required sample size for luke. luke should sample at least people.