Question

13. Show your work for full marks: Forty-five percent of the applications received for a particular credit card are accepted. Among the next ten applications,

   A) What is the probability that all will be rejected?

2. What is the probability that all will be accepted?
3. What is the probability that exactly 4 will be accepted?
4. What is the probability that fewer than 3 will be rejected?
5. What is the probability that more than two will be rejected?(Use Excel to solve and write the function used to obtain the result.)

F) Find the expected number of accepted applications.

G) Determine the standard deviation for the number of accepted applications

Answer 1

P(applicaiton accepted) = 45% = 0.45

n = 10

A) P(x = 10)

P(x = 10) = 0.00034

B) P(x= 4)

P(x= 4) =  0.23837

C) P (fewer than 3 rejected) = P(8 accepted) + P(9 accepted) + P(10 accepted)

P (fewer than 3 rejected) = P(8 accepted) + P(9 accepted) + P(10 accepted)

P (fewer than 3 rejected) = 0.02289 + 0.00416 + 0.00034 = 0.02739

P (fewer than 3 rejected) = 0.02739

D ) P ( more than 2 will be rejected) = P(zero accepted) + P(1 accepted) + P(2 accepted) + (3 accepted) + P(4 accepted) + P(5 accpeted) + P(6 accepted) + P(7 accepted)

which is equal to 1- [ P(8 accepted) + P(9 accepted) + P(10 accepted) ]

P ( more than 2 will be rejected) = 1- [ P(8 accepted) + P(9 accepted) + P(10 accepted) ]

P ( more than 2 will be rejected) = 1- 0.02739 = 0.97261

P ( more than 2 will be rejected) = 0.97261

E) Expected number of acctpeted applications = expected mean = N = 10 *0.45 = 4.5

D) SD