1. Bring your completed exam to class on Monday November 10, 2014, being sure that you have made a copy for safe keeping; OR
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1 PubHlth 540 Fall 2014 Exam III Choice B (Unit 5 Normal) corrected Page 1 of 7 PubHlth Introductory Biostatistics Fall 2014 Examination III Choice B Unit 5 (Normal) Due Monday November 10, 2014 Last submission date for credit: Monday November 17, 2014 Clarification. This is the Unit 5 Test Normal and is Examination III Choice B. Examination III is satisfied with by taking either: Unit 4 Test (Bernoulli and Binomial) or Unit 5 Test (Normal) or both. (1) You submit Examination III Choice A (Unit 4 Test Bernoulli and Binomial); or (2) You submit Examination III Choice B (Unit 5 Test - Normal); or (3) You submit BOTH Examination III Choices A and B Note - If you choose to attempt both choices A and B, I will take the higher grade. Instructions and Checklist: 1. Start each problem on a new page. 2. Write your name on every page. 3. Make a photo-copy of your exam for safekeeping prior to submission 4. Complete the signature page How to submit your exam: Worcester In-Class Section 1. Bring your completed exam to class on Monday November 10, 2014, being sure that you have made a copy for safe keeping; OR 2. Mail your completed exam to me with post mark November 10, 2014 to my address below. Blackboard Learn ONLINE Section 1. Upload your completed exam to the ASSIGNMENT tab no later than 11:59 pm on Monday November 10, This must be a single pdf and be named using the convention lastname_exam3a.pdf. 2. Mail your completed exam to me with post mark November 10, 2014 to my address below. Carol Bigelow School of Public Health/402 Arnold House University of Massachusetts/Amherst 715 North Pleasant Street Amherst, MA Tel
2 PubHlth 540 Fall 2014 Exam III Choice B (Unit 5 Normal) corrected Page 2 of 7 PubHlth Introductory Biostatistics Fall 2014 Examination III Choice B Unit 5 (Normal) DUE: 11:59 PM Monday November 10, 2014 Last submission date for credit: 11:59 PM Monday November 17, 2014 Signature This is to confirm that in completing this exam, I worked independently and did not consult with anyone. Signature: Printed Name: Date:
3 PubHlth 540 Fall 2014 Exam III Choice B (Unit 5 Normal) corrected Page 3 of 7 1. (20 points total) Fill in the blanks. 1a. (2 points) Normal distributions are centered on the value of 1b. (2 points) The total area under a normal distribution curve is exactly 1c. (2 points) What parameter controls the location of a normal distribution curve? 1d. (2 points) What parameter controls the spread of a normal distribution curve? 1e. (2 points) The area under the curve between any two points on a normal distribution curve corresponds to the of values within that range. 1f. (2 points) How many different normal distributions are there? 1g. (2 points) How many different standard normal distributions are there? 1h. (2 points) What is the mean of the standard normal distribution? 1i. (2 points) What is the standard deviation of the standard normal distribution? 1j. (2 points) A random variable that is distributed standard normal is often referred to as a random variable.
4 PubHlth 540 Fall 2014 Exam III Choice B (Unit 5 Normal) corrected Page 4 of 7 2. (20 points total) 2a. (2 points) Consider Z distributed standard normal. What is the value of the 5 th percentile, Z.05? 2b. (2 points) Consider, again, Z distributed standard normal. What is the value of the 95 th percentile, Z.95? 2c. (2 points) Consider, again, Z distributed standard normal. What is the value of the 99 th percentile, Z.99? 2d. (2 points) The 90 th percentile of a normal distribution is how many standard deviations above the mean? 2e. (2 points) The 10 th percentile of a normal distribution is how many standard deviations below the mean? 2f. (2 points) Suppose a certain population of observations is distributed normal. What percentage of the observations in the population are within standard deviations of the mean? 2g. (2 points) Consider again a normal distribution. What percentage of the observations in the population are more than 2.5 standard deviations above the mean? 2h. (2 points) Consider again a normal distribution. What percentage of the observations in the population are more than 3.5 standard deviations away from (above or below) the mean? 2i. (2 points) It is known that Weschler IQ scores are distributed normal with µ = 100 and σ = 15. What is the z-score of a Weschler IQ equal to 95? 2j. (2 points) It is known that the lengths of uncomplicated pregnancies (in weeks) are distributed normal with µ = 39 and σ = 2. What is the z-score of a pregnancy that lasts 36 weeks?
5 PubHlth 540 Fall 2014 Exam III Choice B (Unit 5 Normal) corrected Page 5 of 7 3. (20 points total) Consider again that it is known that the lengths of uncomplicated pregnancies (in weeks) are distributed normal with µ = 39 and σ = 2. You may already know that births occurring before 35 weeks of gestation are considered premature and that births occurring more than 40 weeks gestation are considered post date. 3a. (10 points) What proportion of uncomplicated pregnancies is considered neither premature nor post-date? 3b. (10 points) What are the chances that an uncomplicated pregnancy will result in a premature delivery?
6 PubHlth 540 Fall 2014 Exam III Choice B (Unit 5 Normal) corrected Page 6 of 7 4. (20 points total) Recall that Wechsler IQ scores are distributed Normal with µ = 100 and σ = 15. 4a. (5 points) What Wechsler IQ scores cover the middle 50% of the population of scores? 4b. (5 points) How high must a Wechsler IQ score be to be in the top 10% of scores? 4c. (5 points) How high must a Wechsler IQ score be to rank in the top 1% of scores? 4d. (5 points) An inmate on death row in the state of Illinois has a Wechsler IQ score of 51. What percentage of people have Wechsler IQ scores below this level?
7 PubHlth 540 Fall 2014 Exam III Choice B (Unit 5 Normal) corrected Page 7 of 7 5. (20 points total) Body mass index (BMI) is equal to weight in kilograms divided by height in meters squared. The National Center for Health Statistics estimates that women between the ages of 20 and 29 in the United States have a mean BMI of 26.8 with a standard deviation of 7.4. You may assume that this population of BMI is distributed Normal with µ = 26.8 and σ = a. (10 points) If a BMI of 30 or greater is classified as overweight, what percent of women ages in the United States are overweight according to this definition? corrected b. (10 points) A BMI less than 18.5 is considered to be underweight. What is the probability that a randomly selected woman age in the United States is underweight?
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