Question

Generation Y has been defined as those individuals who were born between 1981 and 1991. A survey by a credit counseling foundation found that 57% of the young adults in Generation Y pay their monthly bills on time. Suppose that we take a random sample of 210 people from Generation Y. What is the probability that 124 or more pay their monthly bills on time?

Answer 1

Let the event of paying monthly bills on time is considered to be a success. The P(success)=0.57

Let X denotes the number of individuals paying monthly bills on time. Then X=0,1,2,3...210.

Now this situation can be treated as a binomial probability condition where all the assumptions of binomial probability is met. But n is quite large so we can approximate the distribution of X to be normal with mean =np and variance=npq.

Here n=210, p=0.57

X~N(119.70,51.47)

The standard deviation will be 7.174

Then we need the

$=P(0.5994<Z<12.58)=0.2746$ =27.46%

So the probability that more than 124 paying the monthly bill is 0.2746