Please show your work

1.A telephone survey uses a random digit dialing machine to call subjects. The random digit dialing machine is expected to reach a live person 15% of the time.

a.True or False:Each call is an independent random event.

In two attempts, what is the probability of achieving......

b.exactly two successful calls? (success = reach a live person)

c.one success and one failure (in any order)?

2.The prevalence of a trait is 76.8%.In a simple random sample of n = 50, how many individuals are expected to exhibit this characteristic and what is the corresponding standard deviation of this estimate?

3.Linda hears a story on National Public Radio stating that one in six eggs in the United States are contaminated with Salmonella. If Salmonella contamination occurs independently within and between egg cartons and Linda makes a three egg omelet, what is the probability that her omelet will contain at least one Salmonella contaminated egg?

4.Suppose that heights of 10-year old boys vary according to a Normal distribution with = 138 cm and = 7 cm.What proportion of 10-year old boys is less than 140 cm in height?

5.A survey selects a simple random sample of n = 500 people from a town of 55,000. The sample shows a mean of 2.3 health problems per person. Based on this information, say whether each of the following statements is true or false. Explain your reasoning in each instance. No calculations necessary.

a.It is reasonable to assume that the number of health problems per person will vary according to a normal distribution.

b.It is reasonable to assume that the sampling distribution of the mean will vary according to a normal distribution.

6.A simple random sample of 18 male students at a university has an average height of 70 inches. The average height of men in the general population is 69 inches. Assume that male height is approximately normally distributed with = 2.8 inches. Conduct a two-sided hypothesis test to determine whether the male students have heights that are significantly different than expected. Show all hypothesis testing steps.

7.True or false? The p-value refers to the probability of getting the observed result or something more extreme assuming the null hypothesis.