. A bank has recently begun a newcredit program. Customers meeting a certain credit requirement canobtain a credit card accepted by participating area merchants thatcarries a discount. Past data show that about 35% of all applicantsfor this card are rejected. If we let X represent the number ofapplicants who are approved for this credit card, the probabilitiesfor the values of X can be calculated using the binomialprobability distribution. Please answer the following questionsbased on the information given in this problem.

a. If 15 individuals apply for thecredit card today what is the probability that none of them will berejected? Show your work.                                          (1point)                                                                                                                    

b. If 15 individuals apply for thecredit card today what is the probability of atmost 5 of them being rejected? Show yourwork.                                     (2 points)     

c. If 15 individuals apply for thecredit card today what is the probability of morethan 12 of them being approved? Show yourwork.                        (2points)           

d. If 15 individuals apply for thecredit card today what is the probability of lessthan half of them being approved? Show yourwork.                     (2points)                                                                                                                                                                                                                                                 

e. If 15 individuals apply for thecredit card today what is the probability of atleast 6 of them being rejected? Show yourwork.                                         (2points)           

f. How many rejections are expectedout of the 15 applications?      (1 point)    

g. Calculate and interpret the standard deviation for the numberof approvals out of the next 15 applications for the credit card.Show your work