Show all work for partial credit. Express probabilities as...

Show all work for partial credit. Express probabilities as decimal values rounded off to 3 significant digits. Use the table of survey results for Problems 1, 2, and 3. If price increases Netflix Amazon Prime Disney+ Max TOTAL Keep 165 136 84 75 460 Cancel 82 64 66 20 232 TOTAL 247 200 150 95 692 1. From the table above, 4 survey results are randomly selected with replacement. Find the probability all 4 were Netflix subscribers. 2. One survey result is randomly selected from the table above. Find the probability the person would cancel after a price increase given they were a Disney+ subscriber. 3. One survey result is randomly selected from the table above. If we chose someone who would keep their subscription after a price increase, what is the probability it was an Amazon subscriber? 4. An advertising agency studied the usage rates for different streaming services. Their results show that among the sample, 22% primarily use Paramount+, 29% primarily use Peacock, and 49% primarily use Hulu. For Paramount+ users, 10% use a borrowed password. For Peacock, 7% use a borrowed password. For Hulu users, 9% use a borrowed password. If we randomly pick someone who uses a borrowed password, what is the probability they use Peacock?

Transcript

00:02 So, in this problem we have a sample of 50 prospective customers and no free premium channels.

00:11 Now in order to answer this we need to know from our previous data that when we have zero channels the probability of subscription was .02.

00:27 So there was a table that was provided with this problem set and the problem set is extensive.

00:34 It goes beyond question number one.

00:38 So with that information now this will make a little bit more sense for calculating.

00:41 So what's the probability that fewer than three customers will subscribe? then we're going to do the probability of zero or one.

01:04 The probability that more than four.

01:09 The other important thing to remember is that we have a sample size of 50 or a trial size if you want to think about it that way.

01:20 So the probability that x is less than three means that we're going to find the probability of zero, one, and two.

01:28 So i'm actually going to jump to part b and do those probabilities first.

01:33 So the probability of zero would be 50 combination zero times .02 to the zero power times .98 to the 50th power.

01:41 The probability of one would be 50 combination one times .02 to the first power times .98 to the 49th power.

01:48 So that's going to give us .3642 plus .3716 and that would be a total of .7358.

02:03 So why i did that one first is because for the probability that x is less than three all i have to do is calculate for the probability of two and add that to my zero and one that i just found.

02:20 So i'm going to take that .7358 plus 50 combination two times .02 to the second power times .98 to the 48th power.

02:35 So that means i'm going to add 2 .7358 .1858 and my probability then would be .9216.

02:53 And then for the probability that more than four customers, so that'd be x is greater than four, i could look at that as one minus the probability that x is less than or equal to three.

03:09 And again, i already have x is less than three.

03:14 So i can calculate this by taking and subtracting .9216 and then whatever the probability for three is.

03:23 So going through that process again, 50 combination three this time.

03:28 So that probability for three is .0607 plus the .9216 means from one i'm going to subtract .9823 to get my probability of .0177.

03:51 So now for part d, if in the actual survey four customers subscribe to the three for all service offer, what does this tell you about the previous estimate of the proportion of customers who would subscribe? it tells us maybe that's, that that is a little bit low.

04:11 So we were assuming that 2%, which would be about one person would do that if they get no premium channels and our actual sample data is showing us it might be a little bit more than that.

04:26 So question two, instead of offering no premium free channels, suppose that two premium free channels are included.

04:32 So now we still have our 50, but now our proportion for two is a .06.

04:42 And then we're going to go through and do our probabilities.

04:45 The probability that x is less than three.

04:47 Now up above, we showed how to do it by hand, but using a graphing calculator or statistical software, we can go ahead and go into second vars and do b binom cdf.

05:04 So with binom cdf, that means binomial cumulative distribution...

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