posted by Xavier on .
In the last senatorial election in New Jersey, the republican candidate got 48% of the vote. During the election an exit poll was conducted by radio station WSTAT. Ten voters selected at random where asked if they voted for the republican candidate.
(a) Let X = "Number of votes for the republican candidate". Give the distribution of X and explain why.
(b) Compute the P(X = 5), P(X < 6), and P(X > 5). Do the calculation directly using doing the calculation directly from the formula or using the Binomial table enclosed.
(c) Give the mean and variance of X. Can we use the normal approximation to the binomial?
(d) Use the normal approximation (regardless of your answer in (c)) to compute the probabilities the P(X = 5), P(X < 6), and P(X > 5) and compare the results with those in part (b).