13. When you sign a contract for a credit card account, do you read it carefully

Question

13. When you sign a contract for a credit card account, do you read it carefully? A survey of a sample of credit card holders asked the following question: « How carefully do you read this contract? » The results showed that 44 % read every single word of it, 33 % read it carefully enough to understand it, 11 % only glanced at it, while 4 % did not read it at all. For this problem, we use a normal approximation for what are essentially four random variables that follow the binomial distribution; out of 500 people who are sampled, how many ‘successes’ are there in the form of the respondent reading every single word of it, etc.

a) In a sample of 500 people, how many ‘successes’ are there in the form of the respondent reading every single word of it?
b) In a sample of 500 people, what is the probability that at least 200 people read every single word of it?
c) In a sample of 500 people, what is the probability that at least 200 people do not read the contract at all?

Explanation / Answer

a)
p = 0.44 , n = 500
Successes = n p = 500 * 0.44 = 220

b)
mean = n p = 500 * 0.44 = 220

std.dev = sqrt(npq)
= sqrt(500 * 0.44 * 0.56)
= 11.0995

P(X > 200)
z = ( x - mean) / s
= ( 200 - 220) / 11.0995
= -1.8019

P(X > 200) = P (z > -1.8019) = 0.9642

c)

mean = n p = 500 * 0.04 = 20

std.dev = sqrt(npq)
= sqrt(500 * 0.04 * 0.96)
= 4.3818

P(X > 200)
z = ( x - mean) / s
= ( 200 - 20) / 4.3818
= 41.079

P(X > 200) = P (z > 41.079) = 0

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