Question

Among all monthly bills from a certain credit card company, the mean amount billed was $485 and the standard deviation was $300. In addition, for 15% of the bills, the amount billed was greater than $1000. A sample of 900 bills is drawn. What is the probability that the average amount billed on the sample bills is greater than $500? What is the probability that more than 150 of the sampled bills are for amounts greater than $1000

Answer 1

Step-by-step explanation:

a.

Let X be the amount paid by a certain credit card service.

From the details supplied, the X-bar is $485, the standard deviation is $300 and n=900.

By the central limit theorem when the sample size is high, the sample mean fits the normal distribution with the mean μ and the standard deviation function

So the likelihood that the total sum paid on the sample bills is greater than $500 is seen.

$P ( x(bar) > 500 )$ = P ( Z > 1.5 )

                         = 1 - 0.93319 { From excel function =NORM.DIST(1.5,0,1,TRUE)

                         = 0.0668

Thus, the probability that the average amount billed on the sample bills is greater than $500 is 0.0668.