Question 4 (15 marks) University students are a major target for advertisements

Question

Question 4 (15 marks) University students are a major target for advertisements for credit cards. At a university, 65% of students surveyed said they had opened a new credit card account within the past year. If 15 students are surveyed, calculate the following probabilities. What is the probability that exactly 6 students opened a new credit card account a) b) What is the probability that more than 12 students opened a new credit card account c) What is the probability that 5 or 6 studen d) What is the probability that 12 or fewer students opened a new credit card account within the past year? (3 marks) within the past year? (7 marks) the past year? (4 marks) within the past year? (1 mark) ts opened a new credit card account within

Explanation / Answer

P = 0.65

n = 15

A) P(x = 6) = 15C6 * (0.65)^6 * (0.35)^11 = 0.0036

B) P(X > 12) = P(x = 13) + P (x = 14) + P(x = 15)

= 15C13 * (0.65)^13 * (0.35)^2 + 15C14 * (0.65)^14 * (0.35)^1 + 15C15 * (0.65)^15 * (0.35)^0 = 0.0617

C) P(x = 5 or 6) = P(x = 5) + P(x = 6)

= 15C5 * (0.65)^5 * (0.35)^10 + 15C6 * (0.65)^6 * (0.35)^11 = 0.01

D) P(X < 12) = 1 - P (X > 12)

= 1 - (P(x = 13) + P(x = 14) + P(x = 15))

= 1 - (15C13 * (0.65)^13 * (0.35)^2 + 15C14 * (0.65)^14 * (0.35)^1 + 15C15 * (0.65)^15 * (0.35)^0)

= 1 - 0.0617 = 0.9383

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