1 In a twocandidate election the population support is evenl

(1) In a two-candidate election, the population support is evenly divided between the two; both
have 50% support. If we where to poll 600 people at random from the population, and let us say that
our random variable X counts the number of people out of the 600 from our poll that support the
candidate, the distribution from such a poll would be approximately normal. Close enough that we
would use the techniques found in Chapter 6. The mean, ?, of the distribution is 300, with a standard
deviation, , of 12.
If we polled 600 people what proportion of the time would we have 318 or more voters support one
candidate versus the other? Assume a normal distribution. Use function notation to represent the
question

Solution

Mean of the distribution = 300

Standard deviation = 12

P(X > 318) = P(Z > (318-300)/12)

= P(Z > 1.5)

= 0.0668