# Math quiz help

Answer the following questions covering materials from previous chapters in your textbook. Each question is worth 2.5 points.

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. In eight attempts, what is the probability of achieving exactly two successful calls?

2. The prevalence of a trait is 76.8%.

a. In a simple random sample of *n* = 5, how many individuals are expected to exhibit this characteristic?

b. How many would you expect to see with this characteristic in a simple random sample of *n* = 10?

c. What is the probability of seeing nine or more individuals with this characteristic in a simple random sample of *n* = 10?

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 µ = 138 cm and σ = 7 cm.

a. What proportion of this population is less than 150 cm tall?

b. What proportion is less than 140 cm in height?

c. What proportion is between 150 and 140 cm?

5. The Wechsler Adult Intelligence Scale scores are calibrated to vary according to a normal distribution with µ = 100 and σ = 15. What Wechsler scores cover the middle 50% of the population? In other words, identify the 25^{th} percentile and 75^{th} percentile of the population.

6. Suppose that scores on the biological sciences section of the Medical College Admissions Test (MCAT) are normally distributed with a mean of 9.2 and a standard deviation of 2.2. Successful applicants to become medical students had a mean score of 10.8 on this portion of the test. What percentage of applicants had a score of 10.8 or greater?

7. A survey selects a simple random sample of *n* = 500 people from a town of 55,000. The sample shows a mean of 2.30 health problems per person (standard deviation = 1.65). Based on this information, say whether each of the following statements is *true* or *false*. Explain your reasoning in each instance.

a. The standard deviation of the sample mean is 0.074.

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

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

8. Ten people are given a choice of two treatments. Let *p* represent the proportion of patients in the patient population who prefer treatment A. Among the 10 patients asked, 7 preferred method A. Assuming there is no preference in the patient population (i.e., *p* = 0.5), calculate P(*X* > 7).

9. 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 σ = 2.8 inches. Conduct a two-sided hypothesis test to determine whether the male students are significantly taller than expected. Show all hypothesis testing steps.

10. True or false? The *p*-value refers to the probability of the data or data more extreme assuming the null hypothesis.

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