Question

Michael is running for president. The proportion of voters who favor Michael is 0.7. A simple random sample of 100 voters is taken.
a. What are the expected value, standard deviation, and shape of the sampling distribution of p?
b. What is the probability that the number of voters in the sample who will not favor Michael will be between 26 and 30?

Answer 1

a) The sampling distribution of proportion obeys the binomial distribution. if the random sample of ‘n’ is obtained with replacement. Such as, if the population is infinite and the probability of occurrence of an event is ‘p’, then the probability of non-occurrence of the event is (1-p).

Given : sample size ‘n=100’ drawn from the population. And 'p=0.7'

Therefore Standard deviation () = √ (p(1-p) / n)

= 0.7(1-0.7)/100

Standard Deviation = 0.0458

The sampling distribution of p is a discrete rather than a continuous distribution. For small p and large n, the binomial distribution approaches symmetry. Here n=100. Therefore the shape of the distribution is a 'Bell Curve'.

b) Note : More Information needed to answer .