Binomial distribution a a supermarket is making purchases...

Binomial distribution A. A supermarket is making purchases. The collection service at the Supermarket during the month of April 2020 reflected that 90% of the customers who make the purchase by Selectos page or app pick it up on time (the day and time assigned). Yes, for a particular day of May, there are 10 purchases to pick up at 1:00 PM. Calculate the following: 1. µ = 2. σ = 3. p = 4. q = 5. P (collect all purchases on time) = 6. P (no more than 2 purchases are picked up on time) = 7. P (no purchases are picked up on time) = 8. P (at least 8 purchases are picked up on time) =

Transcript

00:01 Question we need to compute the mean and the mean here since we have a binomial distribution is the sample size times p which is 10 times 0 .9 which is 0.

00:12 In this case 9 sorry for number 2 we need to compute the standard deviation which by definition of the binomial distribution is n times p times 1 minus here so in our case this is 10 times 0 .9 times 0 .1, which is going to give us 0 .9487.

00:37 Now for item 3, we should compute p.

00:40 P is basically the value of success, so 0 .9.

00:45 And number 4 is q, which is 1 minus p, which is 0 .1.

00:51 Number 5, we should compute what is the probability that o purchases are on time.

00:58 So this here means that each purchase will have a 0 .9 probability to be pick up on time.

01:07 So if you want all of them out of 10, this means that all of them, the first one, the second, and so one until the 10, should be all on time.

01:19 So we keep multiplying by the probability that we have here for each person or purchases.

01:26 So this is the same as 0 .9 at power 10, which is 0 .34 .87.

01:36 Now for number six, we should compute the probability that no more than 2 will be pick up on time.

01:42 So this means that the first, in this case, we could have 0.

01:46 They will not pick, in this case, pick up on time.

01:50 We could have one or two.

01:52 So because i have a binomal distribution, the probability of picking, in this case, none of the purchases on time is given by the combination of the number of purchases.

02:04 Then the number that were like pick up on time, the probability of pick up on time at power of the number that were like on time...

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