The members of a very large health club were observed on a randomly selected day. The distribution of times they spent that day at the health club was found to have a mean of 91.8 minutes and a standard deviation of 16.2 minutes. Suppose these values of the mean and standard deviation hold true for all members of this club.
a. Using Chebyshev’s theorem, find at least what percentage of this health club’s members spend times at this health club between
i. 59.4 and 124.2 minutes
ii. 51.3 and 132.3 minutes
b. Using Chebyshev’s theorem, find the interval that contains the times spent at this health club by at least 89% of members.