1 True or False A discrete random variable X may assume an i

1. True or False: A discrete random variable X may assume an (indefinitely) uncountable number of distinct values.

2. True or False: A cumulative probability distribution of a random variable X is the probability P(X=x), where X is equal to a particular value x.

3. True or False: We use the hypergeometric distribution in place of the binomial distribution when we are sampling with replacement from a population whose size N is significantly larger than the sample size n.

4. Which of the following can be represented by a discrete random variable? A. The number of obtained spots when rolling a six-sided die. B. The height of college students, measured in inches. C. The average outside temperature, in degrees Celcius, taken everyday for two weeks. D. The finishing time, measured in minutes, of participants in a cross-country meet.

5.The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider waits less than three minutes.

6. It is known that the length of a certain product X is normally distributed with (mu)=20 inches and sigma=4 inches. How is the probability P(X>28) related to P(X<16)? A.) P(X>28) is greater than P(X<16). B. P(X>28) is smaller than P(X<16). C. P(X>28) is the same as P(X<16). D. No comparison can be made with the given information.

7. Find the Z value such that P(Z less than or eqaul to z) = 0.9082. A.) z= -1.33 B.) z=0.1814 C.) z= 0.8186 D.) z=1.33 E.) None of these.

8. True or False: The standard deviation of (mean) suggests that the variation between observations is smaller than the variation between averages.

9. If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population? A.) For any sample size n, the sampling distribution of the sample mean is normally distributed. B.) For a sample size n<50, the sampling distribution of the sample mean is normally distributed. C.) For a sample size n<30, the sampling distribution of the sample mean is normally distributed. D.) For a sample size n>30, the sampling distribution of the sample mean is normally distributed. E.) None of these.

10.) Suppose that, on average, electricians earn approximately (mu)= $54,000 per year in the United States. Assume that the distribution for electricians\' yearly earnings is normally distributed and that the standard deviation is (sigma)=$12,000. What is the probability that the sample mean is greater than $66,000?

11.) A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. Approximate the probability that the proportion of students that receive an A is 0.20 or less is____.

12. True of False: Confidence interval for the population mean is wider, the smaller the confidence level.

13. An analyst takes a random sample of 25 firms in the telecommuications industry and constructs a confidence interval for the mean return for the prior year. Holding all else constant, if he increased the sample size to 30 firms, how are the standard error of the mean and the width of the confidence interval affected? A.) Standard error of the mean increases, Width of confidence interval becomes wider. B.) Standard error of the mean increases, width of confidence intervale becomes narrower. C.) Standard error of the mean Decreases, width of confidence interval becomes wider. D.) Standard error of the mean decreases, width of confidence interval becomes narrower. E.) Cannot be determined.

14.) Professors of accountancy are in high demand at American universities. A random sample of 28 new accounting professors found the average salary was $135 thousand with a standard deviation of $16 thousand. Assume the distribution is normally distributed. Construct a 95% confidence interval for the salary of new accounting professors. Give your answers in thousands of dollars.

15.) A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard deviation of 1.12 liters. How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval.

Solution

1. FALSE. It has to be countable.

2. FALSE. It is P(X<=x).

3. FALSE. We do this when the process is WITHOUT REPLACEMENT.

4. A. The number of obtained spots when rolling a six-sided die. [ANSWER]

The height measurement is continuous, because it can take any value including decimals, and so is the temperature and finsihing times.

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