Midterm Study Guide
Name: __________________________
Chapter 3 Review
Date: ________________
Fill in all the missing percentages above and inside the Normal curve below.
99.8%
95%
68%
.1%
2.4% 13.5%
34%
34%
13.5% 2.4%
.1%
Answer the following questions using the Normal curve provided below.
The playing time of a professional soccer player has the normal distribution with mean 55 minutes and standard
deviation 10 minutes.
95%
1. What percentage of on-field time is between 35 and 75 minutes? ________________________.
2. What is the percentage of on-field time greater than 65 minutes? ________________________.
16%
3. How many standard deviations away from the mean is an on-field time of 45? And in which direction (positive or
negative)? ________________________.
-1𝝈
4. How many standard deviations away from the mean is an on-field time of 85? And in which direction (positive or
+3𝝈
negative)? ________________________.
5. What is the percentage of on-field time between 35 and 65 minutes? ______________________.
81.5%
Determine the percentile of the following students based on the list of test grades below.
76 98 78 86 85 80 90 92 87 85 50 93 83 80 70 69 95 83 91 90 89 58 70 80
6. Chris scored a 70.
20.8%
9. Amy scored an 80
7. Jane scored an 83.
50%
10. Charlie scored a 90.
8. David scored a 92.
87.5%
11. Blaire scored an 89.
41.7%
79.2%
70.8%
12. Sydney scored a 78.
29.2%
13. Barley scored a 69.
12.5%
14. Kasey scored a 95.
95.8%
Determine the percentile of the following students based on the list of heights below.
66, 64, 72, 73, 68, 66, 59, 65, 62, 63, 71, 70, 65, 69, 71, 59, 60, 61, 68, 58, 66, 67, 72, 63, 61
15. Jim is 73 inches tall
100%
16. Maggie is 66 inches tall
18. Stephen is 68 inches tall
60%
72%
19. Caroline is 59 inches tall 12%
17. Ralph is 72 inches tall 96%
20. Luke is 61 inches tall
24%
21. Mike is 70 inches tall
22. Ali is 64 inches tall
80%
40%
23. Aiden is 65 inches tall 48%
Use Table A to answer the following questions. Answers should be given with four decimal places.
24. Find the area under the curve less than -1.83
28. Find the area greater than -0.51
25. Find the area between 1.42 and 2.68
29. Find the area between -2 and 1.53
26. Find the area to the right of 2.18
30. Find the area between -0.54 and -1.2
27. Find the area to the left of 0.33
31. Find the area to the left of -1.4
.0336
.9963-.9222= .0741
1-.9854= .0146
.6293
1-.3050= .6950
.9370-.0228= .9142
.2981-.1151=
.1830
.0808
Answer the following questions using standardization.
32. Maria made 76% on her Government test and 83% on her Algebra 2 test. The mean grade on the Government
test was 73% with a standard deviation of 6.2%. The average grade on the Algebra 2 test was 82% with a
standard deviation of 4.5%. On which test did Maria do better?
Government
Algebra 2
z=.483871
z=.22222
Maria did better on Government
33. The mean speed of vehicles along a stretch of highway is 61 mph with a standard deviation of 5.6 mph. You
measure the speed of three cars traveling along this stretch of highways as 62 mph, 57 mph, and 64 mph. Find
the z-score that corresponds to each speed. Determine which car had a relatively faster speed.
1st
z=.1786
The 3rd
2nd
3rd
z=-.714
z=.5357
car had a relatively faster speed
34. The monthly utility bills in a city have a mean of $78 and a standard deviation of $18. Find the z-scores that
correspond to utility bills of $75, $81 and $102. Find the z-score that corresponds to each bill. Determine which
bill had a relatively higher price.
1st
z=-.167
The 3rd
2nd
3rd
z=.167
z=1.33
bill had a relatively higher price