Having trouble with this homework problem, any help is appreciated! Please attac

Question

Having trouble with this homework problem, any help is appreciated! Please attach your work to how you got the answer too, thanks!
1. The mean outstanding credit for adult couples is S650 with a standard deviation of S420. a. What is the probability that a couple chosen at random has a credit balance exceeding S700? b. What is the probability that 100 couples chosen at random has a credit balance exceeding $700? c. The probability that 50 randomly chosen adult couples have an average credit balance greater than a certain average is .29. What is the average amount? d. The probability that 10 randomly chosen adult couples have a total credit balance greater than a certain total is .19. What is the total amount?

Explanation / Answer

a)P(X>700)=P(Z>0.119)=1-P(Z<0.119)=1-0.547=0.453; ( here (700-650)/420=0.119)

b)P(X>700)=P(Z>1.19)=1-P(Z<1.19)=1-0.883=0.117; ( here (700-650)/(420/sqrt(100))=1.19,as 100 samples are taken)

Please note that,In part a) and b) ,values for P(Z<0.119) and P(Z<1.19) respectively are taken from z-table or we can use online calculator for z-score or p-value vice versa)

c) (X-650)/(420/sqrt(50))=1-0.29=0.71

(X-650)/59.4=0.71

X=0.71*59.4+650=692.17

d)

(X-650)/(420/sqrt(10))=1-0.19=0.81

(X-650)/132.81=0.81

X=0.81*132.81+650=757.58

X is an average amount for randomly chosen10 adult couples,hence total amount=757.58*10=7575.8

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