(c) Suppose that 45% of the voting population are Labor voters. A sample of two hundred people is selected at random from the population. Use the normal approximation to the binomial distribution to estimate the probability that more than half of the sample vote Labor.

Question

(c)	Suppose that 45% of the voting population are Labor voters. A sample of two hundred people is selected at random from the population. Use the normal approximation to the binomial distribution to estimate the probability that more than half of the sample vote Labor.

anonymous · Answer

The mean of the approximation is 200 * .45. The std dev of the approximation is 
$$\sqrt{(200 * .45)*(1-.45)}$$

The z score is (x - mu)/sigma or
$$(100-\mu)/\sigma$$

(You calculated mu and sigma above.)

Look up the t-table probability for this z score. (for example, a z score of 2 would be about 95%, 3 would be about 99.7%).  This gives you the probability that the sample will have fewer than 100 Labor voters.

The answer you want is 1 minus this probability.

anonymous · Answer

Ah so you need something like t-table? Can't I use calculator?

anonymous · Answer

Yep, you need a t-table.  I have attached one, although there should be one in the back of your textbook. Some calculators will provide these, but calculating the number yourself is quite complex.