Suppose that only 020 of all computers of a certain type...

Suppose that only 0.20% of all computers of a certain type experience CPU failure during the warranty period. Consider a sample of 10,000 computers. (b) What is the (approximate) probability that more than 10 sampled computers have the defect? (Use the binomial approximation.)

Transcript

00:02 Hello, so this is the information we have, okay? we got n to be 10 ,000 computers with that p to be 0 .2%.

00:11 P will also be 0 .002.

00:17 Okay, so because the because n is very large, we're going to be using the person distribution.

00:26 So person distribution for x equals x, that's going to be n combination.

00:34 Oops, this binomial.

00:38 So for person, that's a negative lambda, this is lambda to the x over x factorial.

00:49 So you can see that we don't have, we don't have lambda, right? so we're going to get lambda, this np, 10 ,000.

01:15 0 .002 what is that going to be four zero is going to go one two three four so that's lambda is going to be 20 and this question is asking us to find the probability of x greater than 10 that is the same as one minus the probability of less than i put 10 so you see here that our x values so our x values are going to range from 0 to 10.

02:04 That's going to be our 8 values.

02:08 And we're just going to substitute all those values in one at a time.

02:16 Get those values, okay? so this is going to go 1 minus you can open a big bracket.

02:22 We're going to do for x equals 0 up to x equals 10.

02:27 So for x equals 0, for example, that's going to be e to the negative.

02:32 Lambda is 20 times 20 x is 0 divided by 0 factorial this for x is 0 and i'm going to go plus therefore x equals 1 we don't have x i'm sorry e to the negative 20 and then times 20 to the 1 over 1 factorial so we're going to do the same thing up to x equals 10 where that is going to be e to the negative 20 times 20 to 10 over 10 factorial.

03:21 Okay, we just need to get those values.

03:29 We're gonna start plugging in numbers.

03:31 We're gonna get 4 x equals 0 now.

03:44 Just a second, set up my calculator.

03:49 Okay, so for this one, x equals 0, we have 2 .06 10 to the negative now.

04:08 For x equals 1, that's going to x equals 1.

04:24 That is going to be 4 .12.

04:33 This is got x equals 2 now.

04:42 2, 2, that is going to be 4 .1, 2, that is going to be 4 .1, 2, it's 10 to the negative 7.

04:59 Plus, we check 3, that's 3 factorial, that's 3, that's 3, that's 3, we have 2.

05:16 0 .74 , minus 10 to the negative 6.

05:25 So now we go to x equals 4, right? then we have 1 .3 ,7.