Suppose 1.5 % of the antennas on new Nokia cell phones are defective. For a random sample of 200

Suppose 1.5 % of the antennas on new Nokia cell phones are...

Key Concepts

Binomial Distribution

The binomial distribution is a probability distribution that applies to experiments with a fixed number of independent trials where each trial has only two outcomes: success or failure. It is characterized by the number of trials (n) and the probability of success (p) on each trial. This distribution is used to calculate the likelihood of obtaining a specific number of successes in a set number of trials using the binomial probability formula.

Binomial Probability Formula

The binomial probability formula, P(X = k) = (n choose k) * p^k * (1-p)^(n-k), is used to determine the probability of observing exactly k successes in n independent trials each with success probability p. It is an essential tool for quantifying the probabilities of different outcomes in problems where events have two outcomes, such as defective or non-defective units.

Complement Rule

The complement rule is a fundamental principle in probability theory that simplifies calculations by using the fact that the sum of probabilities of an event and its complement is one. When computing the probability of events such as 'three or more successes', it can be easier to calculate the probability of the complement event (fewer than three successes) and then subtract this value from one to obtain the desired probability.

Transcript

00:01 All right, so we've got nokia cell phones, and we're supposing that one and a half percent of the antennas are defective on said phones.

00:10 And sampling 12 or 200 antennas, we're going to find some probabilities.

00:17 So what's the probability that none of the antennas are defective and the probability that three or more of the antennas are defective? all right, so this, while this is a, you can see this as a binomial probability, distribution in a binomial experiment, we're going to use the poisson distribution because as n gets large and pi, the probability gets small, we become we go to use a poisson distribution because just as the probabilities are so small that this the limiting factor, the binomial is like the limit or the poison is the limit as as n increases in the binomical.

01:06 Distribution.

01:09 So we i have this stuff here from zero to 10 but we're going to need zero and we don't need to go from zero to 200 because that would be exhaustive.

01:22 What we're going to do instead is look at some complement complements of these events.

01:27 So what we're going to do is use our we need to find the mean which is mu so we'll do that over here.

01:38 You which equals n times pi so 200 times 0 .015 so 3 so mu is 3 and we use that in our formula for our the poisson probability distribution and x is the number so 0 1 2 3 so how many would be defective so we're just going to follow this formula here so it's mu which is 3 to the x power times e but in a spreadsheet it's going to be exp parentheses it's its own function to the negative mu negative three and then we take that and divide it by the x factorial power so we do make a fact that's the formula for factorial in the spreadsheets and it goes all the way down but we don't need it to do that because like i said to go to 200 would be unnecessary.

02:43 We only really need to go through a few of these.

02:47 That should be okay.

02:48 That's enough.

02:51 None of the antennas is defective...

Please give Ace some feedback