Question

Assume that 61% of population in UK vote for Candidate A. The rest of population vote for Candidate B. If we randomly select 36 people in town,
i. What is the center and dispersion of the proportion of voters supporting candidate A in the sample? Can you determine the (approximate) shape of the distribution? Why?
ii. What is the probability that the sample proportion supporting candidate A is less than 60%?
iii. What is the probability that the sample proportion of voters supporting candidate B is greater than 40%?

Answer 1

(I)

(i)

the center of the proportion of voters supporting candidate A in the sample = = 0.61

So

Answer is:

0.61

(ii)

the dispersion of the proportion of voters supporting candidate A in the sample is got as follows:

n = 36

= 0.61

So,

= 1 - 0.61 = 0.39

So,

Answer is:

0.0813

(iii)

The (approximate) shape of the distribution is normal distribution because the sampling distribution of sample proportions is normal distribution for large sample by Central Limit Theorem.

(II)

To find P( < 0.60):
Z = (0.60 - 0.61)/0.0813

= - 0.1230

By Technology, Cumulative Area Under Standard Normal Curve = 0.4511

So,

Answer is:

0.4511

(III)

n = 36

= 0.39

So,

= 1 - 0.39 = 0.61

To find P( >0.40):

Z = (0.40 - 0.39)/0.0813

= 0.1230

By Technology, Cumulative Area Under Standard Normal Curve = 0.5489

So,

P( >0.40):= 1 - 0.5489 = 0.4511

So,

Answer is:

0.4511