## 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)

- In Indiana, 600 8
^{th}-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 - a) In this sample, how many students would be expected to score below Paul?
- b) What percent of the students would be expected to score below John?
- c) What percent of students would be expected to score above Ringo?
- d) How many students would be expected to score below Ringo?
- e) What percent of students would be expected to score below George?
- f) What percent of students would be expected to score above John?
- g) How many students would be expected to score between George and Ringo?
- h) What percent of students would be expected to score between John and Paul?
- i) What percent of students would be expected to score between George and Paul?

- 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

- 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?

- 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.
- a) What size would you expect the largest 85% of all trees to be?
- b) About what percent of the trees should be less than 10 inches in diameter?
- c) About what percent of the trees should be between 9.7 and 10.5 inches in diameter?
- d) About what percent of the trees should be over 11 inches in diameter?

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