Answer to Question #309218 in Statistics and Probability for noel

Question

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?

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

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