c.(1 pt) What is the probability that at least two of the professors in the sample are extroverts?

d.(1 pt) What is the probability that at most four professors in this sample are extroverts?

e.(2 pts) In this group of eight professors selected at random, what is the expected numberof extroverts? What is the standard deviationof the distribution?Show your formula for each.

Franklin UniversityMath215 – Statistical Methods Name: Melanie Talb2.(6 points)The following percentages were obtained over many years of observation by the U.S. Weather Bureau. All data listed are for the month of December.LocationLong-Term Mean % of Clear Days in Dec.Juneau, Alaska18%Seattle, Washington24%Hilo, Hawaii36%Las Vegas, Nevada75%Phoenix, Arizona77%In the locations listed, the month of December is a relatively stable month with respect to weather. Since weather patterns in these locations from one day to the next are more or less the same, it is reasonable to use a binomial probability model.Let r