Question

Problem Binomial Distribution: A consumer advocate claims that 80 percent of cable television subscribers are not satisfied with their cable service. In an attempt to justify this claim, a randomly selected sample of cable subscribers will be polled on this issue.

Suppose that the advocate’s claim is true, and suppose that a random sample of 25 cable subscribers is selected. Assuming independence, find:

(2) The probability that more than 20 subscribers in the sample are not satisfied with their service. Minitab instructions: Go to Calc > select Probability Distributions > select Binomial > select Cumulative probability > Number of Trials insert 25 > Event Probability insert “.8” > Input Constant insert “20.” Click OK.Paste your Minitab results here and then show your work to calculate P(x > 20) = 1 – P(x ≤ 20) to get your final answer:

(3) The probability that between 20 and 24 (inclusive) subscribers in the sample are not satisfied with their service.

(A) Miniab instructions: Go to Calc > select Probability Distributions > select Binomial > select Cumulative probability > Number of Trials insert 25 > Event Probability insert “.8” > Input Constant insert “19.” Click OK.

(B) Minitab instructions: Go to Calc > select Probability Distributions > select Binomial > select Cumulative probability > Number of Trials insert 25 > Event Probability insert “.8” > Input Constant insert “24.” Click OK. Paste each of your Minitab results here and then show your work to calculate P(20 ≤ x ≤ 24) = P( x≤ 24) – P(x≤ 19) to get your final answer:

(4)  The probability that exactly 24 subscribers in the sample are not satisfied with their service.Paste your Minitab results here:

c) Suppose that when we survey 25 randomly selected cable television subscribers, we find that 15 are actually not satisfied with their service. Using a probability you found in this exercise as the basis for your answer, do you believe the consumer advocate’s claim? Explain your answer here:

Answer 1

Question 2.

Solution :-

Just by following the steps given in the question to evaluate the probability of events equals to smaller than 20, we get probability i.e.

Binomial with n = 25 and p = 0.8

x	P( X ≤ x )
20	0.579326

Now we know from the property of probability that sum of probability of disjoint and exhaustive events  =1.

Now P( X ≤ 20)=0.579326, that means P(X>20)=1-0.579326=0.420674 (Answer)

Question 3.

Solution :- We follow the instruction given in the question in two parts to find the probability of event equal to or less than 20 i.e.

Binomial with n = 25 and p = 0.8

x	P( X ≤ x )
24	0.996222

Again we follow the steps given in the next part of the question to obtain the probability of event equals to or less than 19 i.e.

Binomial with n = 25 and p = 0.8

x	P( X ≤ x )
19	0.383311

Now to fins the probability of event between 19 and 24(inclusuve) we need to substract earlier from the later probability. i.e. we need to do the following things.

P(19<x ≤24)=P( X ≤ 24)-P( X ≤ 19)=0.996222-0.383311=0.612911 (Answer)

Question 4

Solution :- To find that exactly 24 are not satsified with service we need to find the following-

P(x=24)=P(x ≤24)-P(x≤23)=0.996222-0.972610=0.023612

Question (c)

Solution :-We find that to check this cliam we need to run the following hypothesis testing.

I am taking one tail test here. we can do teo tail test also.

Becasue in our sample test we get number of people who are unsatisfied =15.

From the matlab we found the area to the left of 15 in binomial cumulative distribution table = 0.0173319

Which is less than 5% i.e. 0.05. Hence we can say that we have enough evidence to reject the null hypothesis. This result is significant at 5% level.