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Name ___ KEY CORRECT SOLUTION IS UNDERLINED ______________________________ Exam 1 Part 1: Chapters 1-3 Math &146 Winter ’10 – Gray Instructions: Show work for each question. Partial credit will be awarded based on work shown. This includes showing what was entered into the calculator and sketching the Normal distributions. To clarify the final solution, box it. There is a 100 minute time limit. A graphing calculator must be used. Each problem is worth 4 points. There are 4 extra credit points possible. Assume all rounding to be at 4 decimal places Problems 1-6 [4 points each] The lengths of pregnancies in a small rural village are Normally distributed with a mean of 265 days and a standard deviation of 13 days. 1. What proportion of pregnancies are longer than 275 days? Normalcdf(275,1E9,265,13)=0.2208 2. How many days is the cut-off for the top 10% of pregnancies? Calculator input is percentage to left. 10% above is same as 90% below. invNorm(0.9,265,13)=281.6602 Days 3. What proportion of pregnancies are longer than 250 days and shorter than 280? Nomalcdf(250,280,265,13)=0.7514 4. Using the 68-95-99.7 Rule, what pregnancies lengths make up the middle 95%? 95% is ±2 ° 265 ± 2 13 ± = 265 ± 26 = 239 to 291 days. 5. Is this distribution considered a standard Normal distribution ? Is not, what mean and standard deviation would make it a standard Normal distribution? No, standard Normal distributions have mean 0 and standard deviation 1. 6. Suppose Ana s pregnancy lasted 270 days. a. What is her z- score? b. If another woman in the hospital gave birth on the same day as she did with a z -score of 0, who conceived first? ? = ?²−³ ° = 270 265 16 = 0.3846 0 < 0.3846 Ana conceived first.
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Exam 1 Math 146 Winter ’10 – Gray Page 2 Problems 7-8 A sample was taken of the verbal SAT scores of applicants to a California State College. The following is a box-plot of the scores. 7. What is the approximate scores for the middle 50% of the verbal SAT scores above? SOLUTION: Verbal GRE scores from approximately 380 to 610. Scores from 400 to 610 (or close are okay). 1 point off it student put approximately 480. 8. State three other useful facts about the box-plot above. In other words, list three pieces of information you can gather from the plot. SOLUTION: A five point summary is good. (Giving approximately Verbal GRE scores is okay.) Min: 280, Q1: 380, Med: 480, Q3: 520, Max: 770. #10 SOLUTION: Removing 1 data point will move the median very little (it will still be in the interval 10 to 20. However it will cause the mean to drop as this data point is very high and influential. (a) is the best choice. #11 SOLUTION: Skewed right means that the median is left of the mean. So, (e) is the best choice. Problems 7-11
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This note was uploaded on 10/15/2011 for the course SPAN 101-103 taught by Professor All during the Fall '11 term at Tacoma Community College.

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