Question

Residents of the Shire, being genearally distrustful of wizards, give Gandalf an approval rating of 37%

Find the probability that fewer than 18 residents of the Shire, taken out of a random sample of 74, approve of Gandalf.

Answer 1

We have given, p = 0.37 and n = 74

np = 74 * 0.37 = 27.38 > 10

n(1-p) = 74 * (1 - 0.37) = 46.62 >10

Therefore we can use here normal approximation to binomial

P[X<18]

=P[X<17.5]..........................using continuity correction.

=P[Z<-2.38]

=0.0087.......................by using normal probability table.

Alternatively directly by using binomial ditribution

with n = 74 , p = 0.37

  =BINOMDIST(17,74,0.37,TRUE)

=0.0072