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Bussiness Statistics

MBA 5210 – Business Statistics

Sessions 7& 8   On-line  Spring 202

 

Work the following problems on separate sheets of paper in necessary and attach to this sheet.   (20 points)

 

  1. In Indiana, 600 8th-grade students in a school district took a standardized social studies test that is Normally distributed and has a mean of 280 and a Standard Deviation of 20. Here are the scores for four of the students: John scored 325, Paul scored 310, George scored 300, and Ringo scored 270
  2. a) In this sample, how many students would be expected to score below Paul?
  3. b) What percent of the students would be expected to score below John?
  4. c) What percent of students would be expected to score above Ringo?
  5. d) How many students would be expected to score below Ringo?
  6. e) What percent of students would be expected to score below George?
  7. f) What percent of students would be expected to score above John?
  8. g) How many students would be expected to score between George and Ringo?
  9. h) What percent of students would be expected to score between John and Paul?
  10. i) What percent of students would be expected to score between George and Paul?

 

 

 

 

 

 

  1. A middle-school student took two standardized tests. On the Language Proficiency test she scored 109.4 (mean = 108, SD = 5) and on Mathematical Reasoning she scored 66.5 (mean = 54, SD = 2). On which test did she do better? Justify your answer

 

 

 

 

 

 

 

  1. Sales of widgets are Normally distributed with a mean of 170 and a standard deviation of 20. We have to sell at least 185 widgets to break even. What is the probability that we will make a profit?

 

 

 

 

 

 

 

 

  1. A forester measured 60 of the trees in a large woods that is up for sale. He found a mean diameter of 12.5 inches and a standard deviation of 2.5 inches. Suppose that these trees provide an accurate description of the whole forest and that a normal model applies.
  2. a) What size would you expect the largest 85% of all trees to be?
  3. b) About what percent of the trees should be less than 10 inches in diameter?
  4. c) About what percent of the trees should be between 9.7 and 10.5 inches in diameter?
  5. d) About what percent of the trees should be over 11 inches in diameter?

 

 

 

 

 

 

 

 

  1. In the overall population, the average IQ score is 100 with a standard deviation of 10.
  2. a) What percentage of the general population have IQ scores higher than 108?
  3. b) What percentage of the general population have IQ scores below 99?
  4. c) What percentage of the scores in a normal distribution are higher than 118?
  5. d) What percentage of the scores fall between 88 and 109?
  6. e) What IQ score has 73% of the scores below it?
  7. f) What IQ score has 55% of the scores above it?