Essay Hypothesis Testing and Confidence Interval Review – Statistics Assignment Help

Assignment Task

1. Suppose that patients who receive an operation on their ankle are asked to rate their post-operative pain on a scale of one to 5. The distribution of their responses is given below.
X 1 2 3 4 5
P(X) .15 .18 .29 .27 .11
 

a.) Find the expected value of the random variable X.

b.) Find the variance and standard deviation of the random variable X.

c.) Find P(X < 4).
 

2. Suppose that 23% of the people in a certain town agree with a proposal to tear down the old town center in order to build a new shopping mall.
a.) If people are randomly selected find the probability that the first person you interview who agrees with the proposal is the 8th person you select.

b.) Find the probability that it takes 4 or fewer people interviewed to find the first person who agrees with the proposal.

c.) Find the probability that it takes more than 6 people interviewed before you find the first person who agrees with the proposal.

d.) Find the mean number of people you would have to interview in order to find someone who agrees with the proposal.

e.) Find the standard deviation of the number of people you would have to interview in order to find someone who agrees with the proposal.

3. Refer to problem #2. Suppose that 20 people are randomly chosen.
a.) Find the probability that exactly 3 of them agree with the proposal.

b.) Find the probability that more than 8 of them agree with the proposal.

c.) Find the probability that fewer than 10 of them agree with the proposal.
d.) Find the mean number of people out of 20 who agree with the proposal.

e.) Find the standard deviation of the number of people out of 20 who agree with the proposal.