Question

Harry Potter books have become popular with children and adults alike. A recent survey conducted in London revealed that 56% high school students have read the first Harry Potter book. A random sample of 15 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) (click to select) ' (n={ x- Round answers for parts (b) and (c) to two decimal places. Round answers for parts (d) through (h) to four decimal places. 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

b)
expected number = 0.56*15 = 8.4

c)
variance = 15*0.56*0.44 = 3.6960

d)
P(X = 2) = 15C2*0.56^2*0.44^13 = 0.0008

e)
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 15C0*0.56^0*0.44^15 + 15C1*0.56^1*0.44^14 + 15C2*0.56^2*0.44^13

= 0.0009

f)
P(X <= 5) = 0.0661
=BINOM.DIST(5,15,0.56,TRUE)

g)
P(2 <= X <= 7) = 0.3176
=BINOM.DIST(7,15,0.56,TRUE) - BINOM.DIST(1,15,0.56,TRUE)

h)
P(X > 7) = 0.6824
=1 - BINOM.DIST(7,15,0.56,TRUE)