(b) The lecturer decides to consider multiple years that they taught the module. Theybelieve that the number of students who fail each year can be described by thebinomial distribution. Discuss whether the binomial distribution is appropriate touse here.(c) The probability distribution for a binomial random variable X ~ binomial(n, p)where n is the number of trials and p the success probability, is:n!P(X = x) =k!(n – k)[P*(1 – p)"-kExplain the role ofn!K(n-k)!in the equation above.(d) After looking at the results for several years they decide that the distributionX ~ binomial(20, 0.1) is appropriate for the number of students who fail the moduleeach year. What is the mean and standard deviation of this random variable?(e) The lecturer is interested in situations when no students fail. What is the probabilityof this occurring.

INTRODUCTION: The Physical conditions of Binomial distribution are listed below. The number of…

Answered: (b) The lecturer decides to consider…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Lawrence likes to shoot a bow and arrow in his free time. On any shot, he has about a 10% chance of hitting the bull's-eye. As a challenge one day, Lawrence decides to keep shooting until he gets a bull's-eye. Let Y = the number of shots he takes. Does this scenario describe a binomial setting? Justify your answer. Yes, this is a binomial setting and X has a binomial distribution with n = 10 and p = 0.10. No, this is not a binomial setting because the probability of success is not the same for each trial. No, this is not a binomial setting because the trials are not independent. No, this is not a binomial setting because there are not a fixed number of trials. No, this is not a binomial setting because the given scenario is not binary.
When a random variable X follows binomial distribution, the probability of a success on one trial is equal to 0.3, and the number of trials is equal to 28, What is the expected value of X?
4. Build the theoretical probability table based on the distribution above. Use the binomial distribution with the theoretical probability and number of trials with each possible value. (To calculate the first value where x = 0, use binomialpdf(n, p, 0), where n and p are your theoretical probability and the number of draws. Do the same thing for x = 1 with binomialpdf(n, p, 1), etc.) x P(x) 0 1 2 3 4 5 6 7 8 9 10
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A company that sells binders decides to run a promotion on their 1-inch and 2-inch size binders. Theydiscount the 1-inch binders to $1 per binder and discount the 2-inch binders to $2 per binder. They limitsales to a quantity of 5 of each size of binder per customer. The probability distribution of “X = the numberof 1-inch binders purchased by a single customer during the promotion period” is given in the table below. X 1 2 3 4 5 P(X) 0.02 0.09 0.12 0.15 0.62 a) Compute the mean and standard deviation of X. b) The company’s cost of manufacturing a single 1-inch binder is $0.25. What is the expected profit (indollars) that the company will make, per customer, for 1-inch binder sales during the promotion? c) The mean and standard deviation of “Y = the number of 2-inch binders purchased by a singlecustomer” is 2.74 and 1.25, respectively. Assume that the number of 1-inch and 2-inch binderspurchased are independent random variables. What are the mean and standard deviation of the…
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A random variable follows a binomial distribution with a probability of success equal to 0.62. For a sample size of n= 7 Find The probability of 4 or more successes Answer : P(X > or equal 4)=
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I. Boston Children’s Hospital estimates that 90% of Americans have had chickenpoxby the time they reach adulthood.32(a) Suppose we take a random sample of 100 American adults. Is the use of the binomial distributionappropriate for calculating the probability that exactly 97 out of 100 randomly sampled Americanadults had chickenpox during childhood? Explain.(b) Calculate the probability that exactly 97 out of 100 randomly sampled American adults had chickenpoxduring childhood.(c) What is the probability that exactly 3 out of a new sample of 100 American adults have not hadchickenpox in their childhood?(d) What is the probability that at least 1 out of 10 randomly sampled American adults have had chickenpox?(e) What is the probability that at most 3 out of 10 randomly sampled American adults have not hadchickenpox?
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