According to a recent poll, about 40% of Americans believe in ghosts. Assuming this percentage is accurate, suppose 20 people were randomly selected and asked if they believe in ghosts and the number saying they do is recorded.(a) Explain why this is a binomial experiment.(b) Find the probability that exactly 9 of those asked believe in ghosts. Do not use statistical features of your calculator.(c) Find the probability that at least 10 of those asked believe in ghosts. You may use any features of your calculator.(d) Find the probability that between 7 and 12 people believe in ghosts inclusive.(e) Compute and interpret the mean number of people that believe in ghosts.(f) Compute the standard deviation for the number of people that believe in ghosts.

As per our guidelines we are suppose to answer only three subparts kindlypost the remaining subparts in next postGivenp=0.40sample size(n)=20a)i)No.of trails "n" is finite ii)All the trails are independent iii)Probability of success "p" is constant in each trail iv)each trail has only two outcomes i.e., sucess or failureso, Binomial distribution is used here x~Binomial(n=20,p=0.40)P(X=x)=(nx)×px×(1-p)n-x ; x=0,1,..,nb)The probability that exactly 9 of those asked believe in ghosts is=P(x=9)=(209)(0.40)9(1-0.40)20-9 where (nx)=n!x!(n-x)!=(20!9!(20-9)!)(0.40)9(0.60)11 =0.1597The probability that exactly 9 of those asked believe in ghosts is 0.1597c)the probability that at least 10 of those asked believe in ghosts is=P(x≥10)=1-P(x<10)=1-[P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)+P(x=7)+P(x=8)+P(x=9)]=1-[100(0.40)0(1-0.40)10-0+101(0.40)1(1-0.40)10-1+102(0.40)2(1-0.40)10-2+103(0.40)3(1-0.40)10-3+104(0.40)4(1-0.40)10-4+105(0.40)5(1-0.40)10-5+106(0.40)6(1-0.40)10-6+107(0.40)7(1-0.40)10-7+108(0.40)8(1-0.40)10-8+109(0.40)9(1-0.40)10-9]where (nx)=n!x!(n-x)!=1-[0.00004+0.00049+0.00309+0.01235+0.03499+0.07465+0.12441+0.16588+0.17971+0.15974]=1-0.75535=0.24465≅0.2447the probability that at least 10 of those asked believe in ghosts is 0.2447

Answered: According to a recent poll, about 40%…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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According to a recent poll, about 40% of Americans believe in ghosts. Assuming this percentage is accurate, suppose 20 people were randomly selected and asked if they believe in ghosts and the number saying they do is recorded.

(a) Explain why this is a binomial experiment.

(b) Find the probability that exactly 9 of those asked believe in ghosts. Do not use statistical features of your calculator.

(d) Find the probability that between 7 and 12 people believe in ghosts inclusive.

(e) Compute and interpret the mean number of people that believe in ghosts.

(f) Compute the standard deviation for the number of people that believe in ghosts.

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