The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 8.3 cm. a. find the probability that an individual distance is greater than 212.50 cm. b. find the probability that the mean for 25 randomly selected distances is greater than 201.20 cm. c. why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

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.