Answer to Question #338923 in Statistics and Probability for Andy

Question #338923

At a suburban shopping mall 70% of customers pay by ecocash.Find the probability that in a randomly selected sample of ten customers : exactly 3 pay by ecocash and more than 6 pay by ecocash

1
Expert's answer
2022-05-09T18:23:50-0400

Let X=X= the number of customers pay by ecocash:XBin(n,p).X\sim Bin(n, p).

Given n=10,p=0.7,q=1p=0.3.n=10, p=0.7, q=1-p=0.3.

1.


P(X=3)=(103)(0.7)3(0.3)103=0.009001692P(X=3)=\dbinom{10}{3}(0.7)^{3}(0.3)^{10-3}=0.009001692

2.


P(X>6)=1P(X=7)P(X=8)P(X>6)=1-P(X=7)-P(X=8)

P(X=9)P(X=10)-P(X=9)-P(X=10)

=1(157)(0.7)7(0.3)107(158)(0.7)8(0.3)108=1-\dbinom{15}{7}(0.7)^{7}(0.3)^{10-7}-\dbinom{15}{8}(0.7)^{8}(0.3)^{10-8}

(159)(0.7)9(0.3)109(1510)(0.7)10(0.3)1010-\dbinom{15}{9}(0.7)^{9}(0.3)^{10-9}\dbinom{15}{10}(0.7)^{10}(0.3)^{10-10}

=0.6496107184=0.6496107184


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment