Question

1. Suppose that 61% of all the city’s voters favor the candidate. Find the probability that in a random sample poll of 18 voters taken in a large city, at least 75% will favor a certain candidate for mayor.

2. Suppose that 61% of all the city’s voters favor the candidate. Find the probability that in a random sample poll of 18 voters taken in a large city, less than 6 will favor a certain candidate for mayor.

Answer 1

1)

here this is binomial with parameter n=18 and p=0.61

P( at least 75% will favor a certain candidate for mayor ):

P(X>=14)=1-P(X<=13)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.1093

if using ti-84 use command :1-binomcdf(18,0.61,13)

if using excel use command :1-binomdist(13,18,0.61,true)

2)

P(X<6)=

∑x=05     (nCx)px(1−p)(n-x)    =

0.0044

if using ti-84 use command :binomcdf(18,0.61,5)

if using excel use command :binomdist(5,18,0.61,true)