5 the probability of selling a promotional product to a...

5. The probability of selling a promotional product to a customer is 20%. In one day, a promoter approaches 50 people. a. What is the probability of selling exactly 20 products? (2) b. What is the probability of selling exactly 50 products? (2) c. What is the probability he will sell at least 10 products? (2) d. What is the probability he will sell at most 10 products? (2) e. We say that an event is unusual if it occurs 5% or less of the times. i. Would it be unusual if he sold 10 products? Show work to support answer. (3) ii. Would it be unusual if he sold 15 products? Show work to support answer (3)

Transcript

00:01 Hey there, welcome to numerate.

00:03 So we are given a problem here that aligns with the binomial probability distribution.

00:09 A person selling a promotional product here, where his probability of successfully selling the product to a customer is around 20%.

00:18 So if he approaches 50 people here, for part a, what's the probability that he sells to exactly 20 people or 20 products? so again, we are given the probability here as 0 .20.

00:36 Our sample size here is that he approaches 50 people.

00:43 And our x value, we're going to see exactly 20 he sells.

00:51 So the probability of 20, we're going to be utilizing the binomial equation.

00:57 So the binomial equation is the number of trials, 50 over x, which is the, basically, the 20 products, right? x is basically the number of successes here.

01:10 So it'll be 20, multiplied by the probability, which we know is 0 .20, raised to the x, which is 20, multiplied by 1 minus 20, it is 0 .80, raised to the 50 minus 20, which is 30.

01:27 So this is our equation here.

01:29 We're going to utilize.

01:31 So for our probability of 20, 20 will give us a probability that equals around 0 .006.

01:50 0 .0006 to 4 decimal places.

01:56 Now for part b we're looking what is the probability of selling exactly 50 products, so 50 out of 50.

02:05 So we're going to utilize the same input here.

02:09 So we have 50 now.

02:11 Exactly 50 equals combinations 54 number of trials 50 for the number of successes we have 0 .20 raised to 20 um 50 sorry times 0 .80 raised to 50 minus 50 is zero so that just simplifies into 1.

02:42 So what this will give us is a probability of getting selling stocky 50 products is around let's see here.

02:58 So it's going to be a very minuscule probability here, but it's going to be approximately zero, but let me see what is the actual decimal here.

03:09 All right, so what we get over here would be 1 .1259 times 10, tuning negative 35, which it could be round to 0 .0 .0 .0 .000.

03:28 0.

03:33 All right.

03:47 Okay.

03:49 Perfect.

03:50 So going on to part c now, we have what is the probability that he would sell at least 10 products? probability of x being at least 10 products.

04:07 So this is basically the probability of 10 plus the probability of 11.

04:13 And we're going to keep on adding our probabilities all the way up to the number of trials here or a sample size.

04:20 Which is basically the probability of 50.

04:24 We're going to use the calculator to compute this one.

04:29 A probability of x being at least 10 would be around 0 .5563...

Question

Please give Ace some feedback