A candidate for public office is thought to have the support

A candidate for public office is thought to have the support of 60% of the voters. A random sample of 100 voters was gathered to verify this position. Use the normal approximation of a binomial to answer the following questions.

A) What are the expected value (mean) and standard deviation for the number of “pro” voters?

B) What is the probability that the number of voters who support the candidate is exactly 50?

C) What is the probability that the number of “pro” voters is more than 70?

D) What is the probability that the number of “pro” voters is between 50 and 65?

Solution

p=0.6

n=100

a)mean=np=60

sd=sqrt(npq)=sqrt(100*0.6*0.4)=4.8989

b) P(X=50) use the correction factor, we get

P(X=49.5)

Use NORM.DIST function in excel, we get 0.008190, here cumulative is used as false

c) P(X>70)=P(X>69.5)

Use NORM.DIST(69.5,60,4.8989,true) and subtract with 1, we get 0.026237

d) P(50<X<65)=P(49.5<X<64.5)

Use normdist fuction as mentioned above for both 49.5 and 64.5, then subtract the two values, we get

0.82084-0.016043=0.804798