Could you please help me solve Problem C - please see the attached files. Please

Question

Could you please help me solve Problem C - please see the attached files. Please help to do it step-by-step with all the workings and solutions. Thank you very much!

PROBLEM C: The College of Business Administration at Acorn University offers a major in Finance. Based on historical records, 30% of the College of Business students major in Finance. A random sample of 20 students is selected. ANSWER QUESTIONS 6 AND 8 BELOW 6. What is the probability that no more than 3 of the selected students are majoring in Finance? 7. What is the probability that at least 16 of the students are not majoring in Finance? 8. What are the mean and the standard deviation of this distribution?

Explanation / Answer

here proportion of students majoring finance=p=30%=0.3

sample size n=20.

let X=number of students majoring finance

we shall use binomial distribution with parameter n=20 and p=0.3 and for Binomial distribution ,P(X=r)=nCrpr(1-p)n-r

(6) P(not more than 3 students)=P(X<=3)=0.1071 ( using ms-excel =BINOMDIST(3,20,0.3,1))

(7) proportion not majoring finance=1-0.3=0.7, here we use binomial distirbution with parameter n=20 and p=0.7

P(X>=16)=1-P(X<16)=1-P(X<=15)=1-0.7625=0.2375

(8) mean=np=20*0.3=6 and standard deviation=sqrt(np(1-p))=sqrt(20*0.3*(1-0.7))=1.3461

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