In: Statistics and Probability
Suppose we have a 20% chance of winning a game and play 30 times. What is the probability we win the game 4-13 times (note: 4 and 13 are included in the interval)? Show your work. If you use a calculator, you must identify the list(s) and/or function(s), with input(s), you used. Give your answer to three decimal places.
Here we see that n=30 is constant, p=0.20 is same for all, events are independent and only two outcomes
Hence binomial distribution is satisfied
x | P(x)=BINOMDIST(x,n,p,0) |
0 | 0.0012 |
1 | 0.0093 |
2 | 0.0337 |
3 | 0.0785 |
4 | 0.1325 |
5 | 0.1723 |
6 | 0.1795 |
7 | 0.1538 |
8 | 0.1106 |
9 | 0.0676 |
10 | 0.0355 |
11 | 0.0161 |
12 | 0.0064 |
13 | 0.0022 |
14 | 0.0007 |
15 | 0.0002 |
16 | 0.0000 |
17 | 0.0000 |
18 | 0.0000 |
19 | 0.0000 |
20 | 0.0000 |
21 | 0.0000 |
22 | 0.0000 |
23 | 0.0000 |
24 | 0.0000 |
25 | 0.0000 |
26 | 0.0000 |
27 | 0.0000 |
28 | 0.0000 |
29 | 0.0000 |
30 | 0.0000 |
So
Using the binomial distribution table we get