Question

Dr. Richmond, a psychologist, is studying the daytime television viewing habits of college students. She believes 48% of college students watch soap operas during the afternoon. To further investigate, she selects a sample of 10.

Develop a probability distribution for the number of students in the sample who watch soap operas.

Find the mean and standard deviation.

What is the probability of finding exactly four students who watch soap operas?

What is the probability four or less of the students selected watch soap operas?

Please explain work!

No. of Students	Probability
0
1
2
3
4
5
6
7
8
9
10

Answer 1

Let, X be the number of college students watch soap operas during the afternoon.

Since , n=10 , p=0.48 , q=1-p=0.52

Here ,

Therefore , the pmf of X is ,

; x=0,1,..............,n

=0 ; otherwise

a) The probability distribution is given by ,

X				P(X=x)
0	1	1	0.001446	0.001446
1	10	0.48	0.00278	0.013344
2	45	0.2304	0.005346	0.055427
3	120	0.110592	0.010281	0.136436
4	210	0.053084	0.019771	0.220396
5	252	0.02548	0.03802	0.244131
6	210	0.012231	0.073116	0.187793
7	120	0.005871	0.140608	0.099056
8	45	0.002818	0.2704	0.034289
9	10	0.001353	0.52	0.007034
10	1	0.000649	1	0.000649
Total				1

b) Mean=np=10*0.48=4.80

c) P(X=4) = 0.220396

d)