43% of adults say cashews are their favorite kind of nut. you randomly select 12 adults and ask each to name his or her favorite nut. find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. if convenient, use technology to find the probabilities.

The ages of personnel in the accounting department of a large company are normally distributed with a standard deviation of 7 years. there is a 0.02275 probability that the age of any randomly chosen person in the department is less than 22 and 0.15866 probabilty that the age of any randomly chosen person is greater than 43. what is the mean of this distribution?