Probability
1. A poll found that 72% of American voters are in favor of a carbon tax. Suppose that six voters in the United States are randomly sampled and asked whether they favor a carbon tax.
a) What is defined as success for this problem?

b) What is the probability, p, of success for each trial?

c) What is the probability of failure for each trial?

d) What is the number of trials?

e) Let random variable x = number of successes. List the possible values of x.

f) Using StatCrunch, determine the probability that the number answering in the affirmative is zero.

g) Determine the probability that the number answering in the affirmative is at least one.

h) Determine the probability that the number answering in the affirmative is between 2 and 4 inclusive.

i) Find the mean, µ, and standard deviation, s, for this binomial distribution.
2. Problem on Page 288

3. A random variable has a probability distribution with a mean, µ = 72, and standard deviation, s = 8.
a. Is the sampling distribution of the sample means for n = 64 a normal distribution? Why?

b. Is the sampling distribution of the sample means for n = 20 a normal distribution? Why?

c. If the probability distribution is a normal distribution, is the sampling distribution of the sample means for n = 20 a normal distribution? Why?
4. Problem 7.71 on Page 324.

a) The distribution of the length of stay is right skewed. A random sample of 80 patients is selected. Find the mean and standard deviation of the sampling distribution of the sample means for n = 80. Is the shape of this sampling distribution approximately a normal distribution? Why or why not?

b) If the sampling distribution is approximately normal, obtain the probability that the sampling error made in estimating the population mean length of stay on the intervention ward by the sample mean of the 80 patients will be at most 2 days.