Payton applies for 12 jobs, each of which he has a 70% chance of getting a job offer for. Assume that job offers are independent of each other.

a. How many job offers is Payton expected to receive?

b. Calculate the probability that Payton receives job offers from all 12 places.

c. Calculate the probability that Payton receives between 5 and 7 job offers.

d. Calculate the probability that Payton receives more than 9 job offers.

e. Calculate the probability that Payton receives fewer than 3 job offers.

f. Calculate the variance of the number of job offer Payton is expected to receive.