Question

Suppose the average outstanding loan for college graduates is $23500 with a standard deviation of $7200. In an SRS of 50 graduating college students, what is the probability that their mean outstanding loan is under $21000?A. .0000B. .0070C. .0141D. .3637E. .9930

Answer 1

Answer:

B. .007

Step-by-step explanation:

Mean=μ=23500

Standard deviation=σ=7200

For sample of 50 students

Mean=μxbar=μx=23500

Standard deviation=σxbar=σ/√n=7200/√50=1018.23

So, the probability that mean outstanding loan for students is under $21000

P(xbar<21000)=P((xbar-μxbar)/σxbar<(21000-23500)/1018.23)=P(Z<-2.455)

P(xbar<21000)=P(Z<-2.455)

P(xbar<21000)=P(-∞<z<0)-P(0<z<-2.455)

P(xbar<21000)=0.5-0.4930=0.007

Thus, the probability that mean outstanding loan for students is under $21000 is 0.007.