Assume that IQ scores are normally distributed, with a standard deviation of 16 points and a mean of 100 points. If 75 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points? (Round your answer to four decimal places.)

An office supply company conducted a survey before marketing a new paper shredder designed for home use. in the survey, 80 % of the people who tried the shredder were satisfied with it. because of this high satisfaction rate, the company decided to market the new shredder. assume that 80 % of all people are satisfied with this shredder. during a certain month, 100 customers bought this shredder. find the probability that of these 100 customers, the number who are satisfied is 69 or fewer.