1. a. P(X = 3) = 0.3125
b. P(X = 1) = 0.0756
c. P(X = 2) = 0.1029
2. a. P(X = 7 ) = 0.1641
b. P(X = 4) = 0.1115
c. P(X < 3) = 0.9734
3. a. 0.2013
b. 0.8791
4. a. The four reasons are:
- There are only two possible outcomes (usually called successes or failures)
- There are a fixed number of trials (n)
- Each trial must be independent of the other trials
- The probabiliy of success (π) is fixed at each trial
b. 0.0988
5. a. 0.0577
b. 0.1335
c. 0.0129
6. 0.9427
7. a. 0.5905
b. 0.3281
c. 0.0815
d. 0.9996
8.
|
n
|
π
|
mean
|
variance
|
standard deviation
|
|
|
a
|
50
|
0.5
|
25
|
12.5
|
3.54
|
|
b
|
20
|
0.25
|
5
|
3.75
|
1.94
|
|
c
|
250
|
0.4
|
100
|
60
|
7.75
|
9. Mean = 2.1 days and standard deviation = 1.21 (to 3 sig.fig.)
10. a.
|
x
|
0
|
1
|
2
|
3
|
4
|
5
|
|
P(X = x)
|
0.17
|
0.36
|
0.31
|
0.13
|
0.03
|
0.00
|
b. E(X) = 1.49
VAR(X) = 1.03 (to 3 sig. fig.)
11. 172.5 cars could be expected to pass the camera and the standard deviation is 11.5.
