IQ scores in a certain population are normally distributed with a mean of 98 and a standard deviation of 14.

Find the probability that a randomly selected person will have an IQ score between 86 and 107.

Find the probability that a randomly selected person will have an IQ score above 84.

A brewery's filling machine is adjusted to fill bottles with a mean of 33.8 oz. of ale and a variance of 0.004. Periodically, a bottle is checked and the amount of ale noted.

Assuming the amount of fill is normally distributed, what is the probability that the next randomly checked bottle contains more than 33.85 oz? (Give your answer correct to four decimal places.)

Let's say you buy 99 bottles of this ale for a party. How many bottles would you expect to find containing more than 33.85 oz. of ale? (Round your answer up to the nearest whole number.) bottles

The weights of ripe watermelons grown at Mr. Smith's farm are normally distributed with a standard deviation of 2.3 lb. Find the mean weight of Mr. Smith's ripe watermelons if only 4% weigh less than 12 lb.

"On hold" times for callers to a local cable television company are known to be normally distributed with a standard deviation of 1.1 minutes. Find the average caller "on hold" time if the company maintains that no more than 6% of callers wait more than 6.7 minutes. (Give your answer correct to two decimal places.)