Practice
Convince yourself that you can comfortably answer these questions either using Minitab
or the table in your text. You are advised to sketch a graph when solving the problems.
Let the random variable Z be distributed by the standard normal distribution.
1. Find P( Z < -2 )
2. Find P( Z > -2 )
3. Find P( Z > 2 )
4. Find P( Z > -1 )
5. Find P( -2 < Z < -1 )
6. Find P( -2 < Z < 1 )
7. Find P( Z < 0 )
8. Find P( Z > 1.96 )
9. Find the 25th percentile of Z.
10. Find the 50th percentile of Z.
11. Find the 75th percentile of Z.
Suppose height X of US males is normally distributed with mean 69 inches and sd 2.
(Hint: Use your answers from problems 1 – 11.)
12. Find P( X < 65 )
13. Find P( X > 65 )
14. Find P( X > 73 )
15. Find P( X > 67 )
16. Find P( 65 < X < 67 )
17. Find P( 65 < X < 71 )
18. Find P( X < 69)
19. Find P( X > 72.92 )
20. Find the 25th percentile of heights.
21. Find the 50th percentile of heights.
22. Find the 75th percentile of heights.
Answers:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
0.0228
0.9772
0.0228
0.8413
0.1359
0.8186
0.5
0.0250
-0.6745
0
0.6745
0.0228
0.9772
0.0228
0.8413
0.1359
0.8186
0.5
0.0250
67.6510
69
22. 70.3490