A credit card company estimated that about 5.6% of customers are not paying thei

Question

A credit card company estimated that about 5.6% of customers are not paying their dues on time. Let X denote the number of customers who are late in paying their dues on time in a sample of 120 customers.

a. The random variable X is i. binomial with n = 120 and p = .56 ii. binomial with n = 120 and p = .056 iii. binomial with n = 120 and the mean 67.2 iv. none of the above

b. LetY denote the number of customers in the sample who pay their dues on time. Then the random variable Y is i. binomial with n = 120 and p = 1.056 = .944 ii. binomial with n = 120 and p = 1.56 = .44 3.1 Binomial Distribution 59 iii. binomial with n = 120 and p = .0944 iv. none of the above

c. The probability of observing at least 110 customers in the sample who pay their dues on time is i. .1361 ii. .9260 iii. .0621 iv. 1P(X 110)

d. The probability P(110Y 116) = .835. This means that i. The chances that 110 to 116 customers in a sample of 120 customers pay their dues late are 83.5% ii. The chances that 110 or 116 customers in a sample of 120 customers pay their dues on time are 83.5% iii. The chances that 110 to 116 customers in a sample of 120 customers pay their dues on time are 83.5% iv. none of the above

Explanation / Answer

Ans:

a) Option ii is correct.

The random variable X is binomial with n = 120 and p = .056

b)Option i is correct.

Then the random variable Y is binomial with n = 120 and p = 1.056 = .944

c)option ii is correct.

P(X>=110)=1-P(X<=109)=1-binomcdf(120,0.944,109)=0.9260

d)Option iii is correct.

The chances that 110 to 116 customers in a sample of 120 customers pay their dues on time are 83.5%.

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