Answer to Question #309954 in Statistics and Probability for Emgee

Question

2. Suppose that the average outstanding credit card balance for young professionals is

Php11,200 with standard deviation of Php 2,600. In simple random sample of 150 young

professionals, what is the probability that the mean outstanding credit card balance does

not exceeds Php12,300?

(HINT: Central Limit Theorem)

Answer 1

Let X be a random variable representing he mean outstanding credit card balance of 150 young professionals, then, according to the central limit theorem, X ~ $N(11200, {\frac {2600^2} {\sqrt {150}}})=N(11200, 743^2)$

$P(X<12300)=P(N(11200,743^2)<12300)=P(11200+743N(0,1)<12300)=P(N(0,1)<1.48)=0.93056$