Answer to Question #345612 in Statistics and Probability for Marmou

Question

Suppose that the average outstanding credit card balance for your professionals is P11,200 with a standard deviation of P2,600. In a simple random sample of 150 young professionals, what is the probability that the mean outstanding credit card balance does not exceeds P11,800?

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 ~ $N(11200, {\frac {2600^2} {\sqrt {150}}})=N(11200, 743^2)$

$P(X<11800)=P(N(11200,743^2)<11800)=P(11200+743N(0,1)<11800)=P(N(0,1)<0.8075)=0.791$

(We found P using z-score table)