Question

The probability of getting an A is 0.15. Find the following if there are 20 students.

a) mean

b) standard deviation

c) atleast 2 get an A

d) No less than 5 get an A

Answer 1

Let X be the number of students who get A.

Then X~Binomial(20,0.15)

X	P(X=x)
0	0.0387595
1	0.1367983
2	0.2293384
3	0.2428289
4	0.1821217
5	0.1028452
6	0.0453729
7	0.0160140
8	0.0045922
9	0.0010805
10	0.0002097
11	0.0000336
12	0.0000045
13	0.0000005
14	0.0000000
15	0.0000000
16	0.0000000
17	0.0000000
18	0.0000000
19	0.0000000
20	0.0000000

A)

The population mean is computed as:

B)

The population standard deviation is computed as:

C)

P(X>=2) = 1-P(X=0)-P(X=1) = 1- 0.0388-0.1368=0.8244

D)

P(X>=5) = 0.1702

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!