Question

From previous research, 75% of hotels offer free wifi in their guest rooms. Consider a random and independent sample of 12 hotels. Use this situation to answer the questions below.
					(a)	Recognizing that this is a binomial situation, give the meaning/values of S, F, n, p, and q.
	S is:			n =
	F is:			p =
				q =
(b)	Construct the complete binomial probability distribution for this situation in a table at the right.
(c)	Find the probability 8 of the hotels offer free wifi in guest rooms.
(d)	Find the probability more than 10 offer free wifi in guest rooms.
(e)	Find the mean and standard deviation of this binomial probability distribution.
(f)	By writing a sentence, interpret the meaning of the mean found in (e).
(g)	Would it be unusual for exactly 11 of the 12 hotels to offer free wifi in guest rooms? Explain your answer.

Answer 1

S: hotel offers free wi fi

F: Hotel does not offers free wi fi

n=12

p=0.75

q=0.25

b)

x	P(x)
0	0.0000
1	0.0000
2	0.0000
3	0.0004
4	0.0024
5	0.0115
6	0.0401
7	0.1032
8	0.1936
9	0.2581
10	0.2323
11	0.1267
12	0.0317

c)

  probability 8 of the hotels offer free wifi in guest rooms =0.1936

d)

probability more than 10 offer free wifi in guest rooms =P(X=11)+P(X=12)=0.1584

e)

mean =np=12*0.75=9

std deviation =sqrt(np(1-p))=1.5

f)this tells us that if a large number of samples of 12 hotel is to be taken then on average 9 will provide free wifi in guest rooms

g)

No as probability of this happening is more than 0.05/