Suppose 100 geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of the balance scale, not all the readings are identical. The results are found to closely approximate a normal curve, with mean of 37 grams and standard deviation of 1 gram. Find the number of students reporting readings in these ranges:
1. more than 37 grams
2. more than 36 grams
3. more than 35 grams
4. more than 38 grams
5. between 36 and 38 grams
6. between 35 and 39 grams
7. between 38 and 39 grams
8. between 36 and 39 grams
9. within 1 gram of the mean
10. more than 2
grams from the mean
On standard IQ tests, the mean is 100 with a standard deviation of 15. The results come very close to fitting a normal curve. Suppose an IQ test is given to a very large group of people. Find the percent of people whose IQ scores fall into the following categories:
11. more than 100
12. less than 100
13. greater than 115
14. between 85 and 115
15. between 70 and 130
16. between 55 and 145
17. less than 55
18. more than 145
The Acme light bulb has an average life of 500 hours with a standard deviation of 100 hours. The length of life of a bulb can be closely approximated by a normal curve. An amusement park buys and installs 10,000 such bulbs. Find the total number that can be expected to last the following amounts of time:
19. at least 500 hours
20. less than 500 hours
21. between 500 and 650 hours
22. between 300 and 500 hours
23. between 650 and 780 hours
24. between 290 and 540 hours
25. less than 740 hours
26. more than 300 hours
27. more than 790 hours
28. less than 410
hours
Percentiles are scores
indicating the fractional part of a distribution that is less than a certain
score. For example, the 20th percentile is the score greater than
or equal to exactly 20% of the scores. The 75th percentile is the
score greater than or equal to 75% of the scores.
29. What percentile is the median score?
30. Assume a certain distribution is normal with mean of 65 and standard deviation of 10.
a. Find the 50th percentile score.
b. Find the 84th percentile score.
c. Find the 97.5th
percentile score.
The z-score for a distribution is found by subtracting the mean from the raw score and dividing the result by the standard deviation. z-scores can be used to compare students' performances, or to compare the performance of one student with that of the entire class. Here are Ms. Smith's class scores for 2 math tests.
31. On which test
did Karen do better relative to the entire class?
| Student | Test 1 | Test 2 |
| Karen | 85 | 89 |
| John | 72 | 93 |
| Hal | 89 | 96 |
| Lora | 75 | 65 |
| Jim | 79 | 79 |
| Beth | 86 | 60 |