Question

Harry Potter books have become popular with children and adults alike. A recent survey conducted in London revealed that 64% high school students have read the first Harry Potter book. A random sample of 12 London high school students is taken, and the number of students who have read the first Harry Potter book is recorded.

a) Define the random variable of interest and give its distribution, including the values of all the parameters.                          

X = (Click to select)Probability that a London high school student has read the first Harry Potter bookNumber of London high school students who read the first Harry Potter bookSample size of London high school students who participated in the surveythe sample mean

X ~ (Click to select)ContinuousNormalUniformBinomial(, )

(Round all probability answers to four decimals)

b) What is the expected number of randomly selected students who have read the first Harry Potter book?     

c) What is the variance of number of students who have read the first Harry Potter book?     

d) What is the probability that exactly two of the randomly selected students has read the first Harry Potter book?

                                                               

e) What is the probability that at least two of the randomly selected students have read the first Harry Potter book?

f) What is the probability that no more than five of the randomly selected students have read the first Harry Potter book?

  

g) What is the probability that between two and seven (inclusive) of the randomly selected students have read the first Harry Potter book?  

h) What is the probability that more than seven of the randomly selected students have read the first Harry Potter book?  

Answer 1

SolutionA:

xis a random variable high school students have read the first Harry Potter book

X~B(12,0.64)

n=12

p=0.64

q=1-0.64=0.36

b) What is the expected number of randomly selected students who have read the first Harry Potter book?

E=np=12*0.64=7.68

c) What is the variance of number of students who have read the first Harry Potter book?   

var=npq=12*0.64*(1-0.64)

=12*0.64* 0.36

=2.7648

d) What is the probability that exactly two of the randomly selected students has read the first Harry Potter book?

P(X=2)=12*c2*0.64^2*0.36*12-2

=0.001

ANSWER:0.001