Math 12 Fall 2011 Name Exam Score: /75 Total Class Percent to Date Exam 3 For problems 1-10, circle the letter next to the response that best answers the question or completes the sentence. You do not have to show any work or write any explanations here. Make sure to read each statement carefully! (2 pts each) 1. The normal probability distribution is applied to: A) a discrete random variable B) a continuous random variable C) any random variable D) a subjective random variable 2. The probability that a continuous random variable x assumes a single value is always: A) less than 1 B) greater than zero C) equal to zero D) between zero and 1 3. Which of the following is not a characteristic of the normal distribution? A) The total area under the curve is 1.0 B) The curve is symmetric about the mean C) The value of the mean is always greater than the value of the standard deviation D) The two tails of the curve extend indefinitely 4. For the standard normal distribution, the z value gives the distance between the mean and a point in terms of the: A) mean B) standard deviation C) variance D) center of the curve 5. As the sample size increases, the standard deviation of the sampling distribution of the sample mean: A) increases B) decreases C) remains the same D) none of these
6. A continuous random variable x has a right-skewed distribution with a mean of 43 and a standard deviation of 8. The sampling distribution of the sample mean for a sample of 20 elements taken from this population is: A) approximately normal B) normal C) skewed to the right D)skewed to the left 7. A continuous random variable x has a right-skewed distribution with a mean of 84 and a standard deviation of 14. The sampling distribution of the sample mean for a sample of 60 elements taken from this population is: A) approximately normal B) not normal C) skewed to the right D)skewed to the left 8. You can make the width of a confidence interval smaller by: A) lowering the confidence level or decreasing the sample size B) lowering the confidence level or increasing the sample size C) increasing the confidence level or decreasing the sample size D) increasing the confidence level or increasing the sample size 9. An employee of the College Board analyzed the mathematics section of the SAT for 92 students and finds x = 32.4 and s = 13.3. She reports that a 97% confidence interval for the mean number of correct answers is (29.391, 35.409). Does the interval (29.391, 35.409) cover the true mean? A) Yes, (29.391, 35.409) covers the true mean B) No, (29.391, 35.409) does not cover the true mean C) We will never know whether (29.391, 35.409) covers the true mean. 10. From a random sample of 19 persons selected from a city, we found that the mean federal income tax paid last year was $4275 with a standard deviation of $766. If we want to construct a 95% confidence interval from this information we A) could use the ZInterval program on our TI83/84 calculators B) could use the TInterval program on our TI83/84 calculators C) could use the 1-PropZTest program on our TI83/84 calculators D) don't have enough information to construct a confidence interval
For problems 11-13, you must draw a picture corresponding to the problem, with correctly labeled axis, and shaded region. You also need to state what calculator program you are using for your calculations. 11. Find the area to the right of z = 1.9. (3 pts) 12. Let x be a continuous random variable that has a normal distribution with a mean of 25 and a standard deviation of 6. Find the value of x so that the area under the normal curve between µ and x is 0.1234 and x is less than µ. Round to two decimals. (3 pts) 13. Find the value of t for the t distribution with a sample size of 16 and the area in the left tail equal to 0.025 (3 pts)
For problems 14-18 you need to show work in order to receive credit! Make sure to clearly state what parameters, formulas and calculator programs you are using, and include pictures of appropriate distributions. Write your answers using a complete sentence with correct units, that indicates that you understand the answer. 14. We know that the length of time required for a student to complete a particular aptitude test has a normal distribution with a mean of 41 minutes and a variance of 3 minutes. What is the probability, rounded to four decimal places, that a given student will complete the test in more than 37 minutes but less than 44 minutes? (5 pts) 15. The number of hours spent per week on household chores by all adults has a mean of 27.3 hours and a standard deviation of 9.5 hours. The probability, rounded to four decimal places, that the mean number of hours spent per week on household chores by a sample of 60 adults will be more than 26.75 is: (7 pts)
When finding a confidence interval, you have to use appropriate formulas, but feel free to use your calculator's interval programs as a check. 16. The world's smallest mammal is the bumblebee bat, also known as Kitti's hog-nosed bat. Listed below are weights (in gram) from a sample of these bats. (15 pts) 1.7 1.6 1.5 2.0 2.3 1.6 1.6 1.8 1.5 1.7 2.2 1.4 a) Assuming that the weight of all bumblebee bats have a normal distribution, construct a 90% confidence interval for the mean weight of all bumblebee bats. Round to two decimal places. b) What is the point estimate? c) What is the margin of error?
17. A simple random sample of 868 persons showed that 17.7% do not have any health insurance. Based on this sample, find the 99% confidence interval for the proportion of all persons who do not have any health insurance, rounded to four decimal places. (9 pts) 18. The Labor Bureau wants to estimate, at a 90% confidence level, the proportion of all households that receive welfare. Find the most conservative estimate of the sample size that would limit the margin of error to be within 0.027 of the population proportion. (10 pts)