For Rey Writer

statistics

MAT 151

M6A1

14 Points

1.Bob made 116 on his accounting midterm and 82 on his biology midterm. For the accounting midterm, the mean score was 102 with standard deviation 14. For the biology midterm, the mean score was 70 with standard deviation of 5. Which score was the higher with respect to the rest of the class? Explain your answer.

Answer questions 2 – 5 dealing with the life expectancy of light bulbs whose lifetimes are normally distributed with a mean life of 750 hours and with a standard deviation of 80 hours.

2.What percent of light bulbs will last longer than 870 hours?

3.What percent of light bulbs will last between 730 hours and 850 hours?

4.What percent of light bulbs will last less than 770 hours?

5.If the quality control program of the company can consistently eliminate the worst 10% of the bulbs manufactured, the manufacturer can safely offer customers a money-back guarantee on all lights that fail before __________ hours of burning time.

An investigator polls a representative sample of common cold sufferers, asking them to estimate the number of hours of physical discomfort caused by their most recent cold. Their estimates approximate a normal curve with a mean of 83 hours and a standard deviation of 20 hour (Problems 6-10)

6.What proportion of sufferers estimate that their colds lasted for longer than forty-eight hours?

7.What proportion suffered for fewer than 61 hours?

8.What proportion suffered for between one and three days?

9.What is the estimated number of hours for the shortest-suffering 10 percent?

10.A medical researcher wishes to concentrate on the 20 percent who suffered the most. She will work only with those who estimate that they suffered for more than _____hours.-

A group of statistics students took a midterm exam. The class mean was 72 and the standard deviation was 3.2. The instructor decided to “curve” the grades. Assuming that the distribution of grades was normal, the instructor decided to assign grades the following way:

Students whose test grades are within 1/2 standard deviation of the class mean will receive C’s.

B’s and D’s will be given to scores from (and including) 1/2 standard deviation up to (and including) 1 1/2 standard deviations above and below the mean respectively.

A’s and F’s will be given to scores above and below 1 1/2 standard deviations of the mean respectively. (Problems 11 – 14)

11. What percentage of students will receive each grade?

A’s:

B’s:

C’s:

D’s:

F’s:

12. What grade would a student with a score of 70 make?

13. What grade would a student with a score of 86 make?

14. Devise a grading scale for the test. Values should be rounded to the nearest ones’ place. Remember that no grades may exist in more than one category.