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Let $x$ be a binomial random variable for $n=30$ and $p=0.1.$a. Explain why the normal approximation is not reasonable.b. Find the function used to calculate the probability of any $x$ from $x=0$ to $x=30$c. Use a computer or calculator to list the probability distribution.

a. cannot use the normal distributionb. $\left(\begin{array}{c}30 \\ x\end{array}\right)(0.1)^{x}(0.9)^{30-x}$c. $P(x)=\operatorname{BINOMDIST}(x, n, p, 0),$ for $x=0$ to $x=30, \quad n=30$ and $p=0.1,$ we get the following probabilities.

Intro Stats / AP Statistics

Chapter 6

Normal Probability Distributions

Section 5

Normal Approximation of the Binomial

The Normal Distribution

University of North Carolina at Chapel Hill

Cairn University

Idaho State University

Lectures

01:36

Suppose that $x$ has a bin…

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For n = 100 and 1 =0.4, us…

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Assume that x is a binomia…

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a. Use a computer or calcu…

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Basic Computation: Normal …

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for this problem were given a binomial distribution of 30 trials and probability of success, No. 0.1. And for part, they were asked to explain why the normal approximation is not appropriate. So the rule of thumb is if n. Times p and n times Q are both greater than or equal to five than the normal approximation is reasonable. So if we calculate an Times P, we get three, which is less than five. So therefore, the normal approximation is not reasonable. We don't have to go on calculate N Times Q. At this point, we've already failed the criteria in here, so let's just list Q Vic would. One minus p was 0.9. So that's part A. And for Part B were asked to find the function that would be used to calculate the probability of any number of successes from a sample of 30 from from a number of 30 trials. So the probability of getting X successes and 30 trials is equal to NGOs. X. This is the generic formula. Times P to the exponents x times Q to the exponents and minus X, and that is for X equals 01 to you any number right up to X right up to the end. So we know end and we know P and we know cues so we can substitute those into our function. So we have the probability of X successes is equal to 30. Choose X time 0.1 to the exponents. X times 0.9 to the exponents. 30 minus X for X is equal to zero 12 any number of to 30. So that's part B. That's their function. And then, in part C, where Ste is a computer or calculator to give a list of the probability distribution. So you can do this in many tab or Excel or on your calculator. I'm gonna show you how to do it in many tab so we can go to calculate make patterned data. What we want is just We're going to start with a list a sequence of numbers from zero through 30 simple set of numbers. We're going to store this pattern in column C one. So the first that first value is zero. The final value is 30 in steps of one, so that will give us a sequence of 0123 up to 30 hit, Okay, and now you can see that a stored in column C one. So then, to figure out the binomial distributions for each of those numbers of successes, we can go to calculate probability distributions by no meal and enter the relevant data. So I have select probability. We don't want cumulative probability. We want the probability for each successive X from 0 to 30. So we have a binomial distribution information entered number of trials is 30 p a 0.1, and we use the column C one, which we just generated previously as the input column. So that's the sequence of numbers from 03 30 and then we will store our calculations in column C two. So we hit okay, and then you can see in column C two are the probabilities. So column C one All right could represent number of successes and column C two are the probabilities associated with those number of successes. So the probability of getting five successes is 0.102 to 3. So column C one and C two represent our list of probability distribution

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