For each of the following situations, tell whether or not the specific random va
ID: 3364610 • Letter: F
Question
For each of the following situations, tell whether or not the specific random variable X has a binomial distribution. If the random variable X does have a binomial distribution, X ~B(n, p), give its description, i.e., indicate the values of n and p. If it does not, explain why not. Which of the five characteristics of a binomial distribution are not satisfied? State at least one.
3. At the Bandelier National Monument in New Mexico, archaeological excavations have uncovered many chipped stone tools made by Native Americans who lived at the site between A.D. 1100 and A.D. 1600. About 15% of these tools are made of obsidian. An archaeologist randomly selects 50 chipped stone tools from this site, a small fraction of the total number of tools uncovered. Let X be the number of these tools that are not made of obsidian.
Warning: Please take notice of the meaning of X - the number of these tools that are not made of obsidian.
(a) The distribution of X is binomial with n = ___________ and p = ____________ Or (b) The distribution of X is not binomial because ....
Explain:
4. A gumball machine contains 25 plastic containers with small toys. Johnny wants the small spider that is in one of the containers so that he can scare his sister. There is only one container that has a small spider. He has four quarters, so he buys four of these containers, which are selected at random, one at a time, by the machine. Let X be the number of spiders he gets - either zero or one.
(a) The distribution of X is binomial with n = ___________ and p = ____________ Or (b) The distribution of X is not binomial because ....
Explain:
Explanation / Answer
Solution :
For each of the following situations, tell whether or not the specific random variable X has a binomial distribution. If the random variable X does have a binomial distribution, X ~ B(n, p), give its description, i.e., indicate the values of n and p.
Part 3. At the Bandelier National Monument in New Mexico, archaeological excavations have uncovered many chipped stone tools made by Native Americans who lived at the site between A.D. 1100 and A.D. 1600. About 15% of these tools are made of obsidian. An archaeologist randomly selects 50 chipped stone tools from this site, a small fraction of the total number of tools uncovered. Let X be the number of these tools that are not made of obsidian.
We are given that : X = the number of these tools that are not made of obsidian.
probability of tools that are made of obsidian = 0.15
Then
p = probability of these tools that are not made of obsidian = 1 - 0.15 = 0.85
n = number of trials = Number of chipped stone tools randomly selected = 50
Since all chipped stone tools are different , hence they are independent
Thus
a) The distribution of X is binomial with n = 50 and p = 0.85
Part 4. A gumball machine contains 25 plastic containers with small toys. Johnny wants the small spider that is in one of the containers so that he can scare his sister. There is only one container that has a small spider. He has four quarters, so he buys four of these containers, which are selected at random, one at a time, by the machine. Let X be the number of spiders he gets - either zero or one.
There are 4 containers and each container has 25 small toys.
Out of these 4 containers , only one container contains small spider.
These 4 trials are not independent , since probability changes for each trial.
That is : for first trial , Probability of one spider in any one out of 4 container is 0.25 and probability of getting 1 spider out of 25 toys is 1/25
For second trial , this probability changes , since for second trail we have 3 containers , so probability of small spider in any one out of 3 containers is 1/3 =0.33
Thus X = number of spiders he gets is not Binomial , because probability of each trial is not same and trials are not independent .
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