Question

4. 30% of the customers at XYZ Stores use a debit card to pay for their purchases. In a recent market research study, 12 of the Store’s over 20,000 customers on record was randomly selected for two focus groups on new payment technologies. a. Is the selection of 12 customers a binomial experiment? Please explain. Ans: b. What is the probability that 5 of the 12 customers selected use a debit card to pay for their purchases? c. What is the probability that at least 4 of the 12 customers selected use a debit card to pay for their purchases? d. What is the probability that at most 4 of the 12 customers selected use a debit card to pay for their purchases?

Answer 1

Answer:

a)

Given,

sample n = 12

p = 0.30

The selection of 12 is Binomial distribution with parameters n , p

P(X = r) = nCr*p^r*q^(n-r)

nCr = n!/(n-r)!*r!

b)

P(X = 5) = 12C5*0.30^5*0.70^7

= 0.1585

c)

P(X >= 4) = 1 - P(X < 4)

= 1 - [P(0) + P(1) + P(2) + P(3)]

= 1 - [12C0*0.30^0*0.7^12 + 12C1*0.3^1*0.7^11 + 12C2*0.3^2*0.7^10 + 12C3*0.3^3*0.7^9]

= 1 - [0.0138 + 0.0712 + 0.1678 + 0.2397]

= 0.5075

d)

P(X < 4) = P(0) + P(1) + P(2) + P(3)

= 12C0*0.30^0*0.7^12 + 12C1*0.3^1*0.7^11 + 12C2*0.3^2*0.7^10 + 12C3*0.3^3*0.7^9

= 0.0138 + 0.0712 + 0.1678 + 0.2397

= 0.4925