Twenty percents of defective wired control panels were...

Twenty percents of defective wired control panels were mistakenly installed on the large automateded machine tools. It is uncertain which of the machine tools have the defective panels, and a sample of six tools is randomly chosen for inspection. Calculate the probability of the following conditions. (a) Sample will include one defective panels, (3 marks) (b) The first defective panel is found in the third inspection, (3 marks) (c) The third defective panel is found in the fifth inspection. (3 marks) (d) At most sixteen panels are defective after tested 100 wired control panels. (7 marks)

Transcript

00:01 In this situation, they tell us that eight machines, three of them have defective panels.

00:06 And we're going to take a sample of the four machines and want to see what probabilities are that some of these machines have the defective panels.

00:14 So the first thing we're going to do here is recognize that this is a binomial situation.

00:19 We have two possible outcomes.

00:23 It either has the defective panel or not.

00:26 And the machines are independent of each other.

00:30 And we have a certain limited amount of trial which is four.

00:33 So this is going to be a binomial situation with n equals to four because we're going to test it in four and with a probability of having the defective machine a three out of eight because three out of eight of the machines have the defective panel.

00:50 So with that in mind we're going to use the binomial distribution here, binomial and all graphical calculators in the statistical module, have a binomial pdf to calculate one type of probabilities and cdf to calculate other.

01:08 So we'll see which ones we have to do.

01:11 So the first question they ask is what is the probability of the sample will include one defective? so the probability in x is equal to one and we write here a binomial that has four trials with three eighth probability of defectives.

01:27 So in this one we use the binomial pdf of your calculations.

01:32 If you use a ti84, you go to distributions, so in the ti84 you go to distributions and in the distributions you're going to look for the binomial binom pdf.

01:49 Pdf is used when we want a specific quantity of results, in this case exactly one defective.

01:56 So that's the one we use...

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