Question

Please answer all parts clearly. Any work guidance is very appreciated!

For questions 1-3, X has a binomial distribution with n = 13 and p = 0.08.

For questions 4-6, X has a binomial distribution with n = 11 and p = 0.24.

1) What is P(X = 0)?

2)What is P(X = 1)?

3)What is P(X > 4)?

4)What is P(X = 0)?

5)What is P(X = 1)?

6)What is P(X > 3)?

Answer 1

Ans:

For n=13 and p=0.08

P(x=r)=13C_r*0.08^r*(1-0.08)^13-r

x	p(x)
0	0.3383
1	0.3824
2	0.1995
3	0.0636
4	0.0138
5	0.0022
6	0.0003
7	0.0000
8	0.0000
9	0.0000
10	0.0000
11	0.0000
12	0.0000
13	0.0000

1)P(x=0)=13C₀*0.08⁰*(1-0.08)¹³=0.3383

2)P(x=1)=13C₁*0.08¹*(1-0.08)¹²=0.3824

3)P(x>4)=1-P(x<=4)=1-P(x=0)-P(x=1)-P(x=2)-P(x=3)-P(x=4)

=1-0.3383-0.3824-0.1995-0.0636-0.0138

=0.0024

For n=11 and p=0.24

P(x=r)=11C_r*0.24^r*(1-0.24)^11-r

x	p(x)
0	0.0489
1	0.1697
2	0.2680
3	0.2539
4	0.1603
5	0.0709
6	0.0224
7	0.0050
8	0.0008
9	0.0001
10	0.0000
11	0.0000

4)P(x=0)=11C₀*0.24⁰*(1-0.24)¹¹=0.0489

2)P(x=1)=11C₁*0.24¹*(1-0.24)¹⁰=0.1697

3)P(x>3)=1-P(x<=3)=1-P(x=0)-P(x=1)-P(x=2)-P(x=3)

=1-0.0489-0.1697-0.2680-0.2539

=0.2595