Question

In: Statistics and Probability

We discussed towards the end of last class (01-11-18) a Poisson problem. This an adaptation of...

We discussed towards the end of last class (01-11-18) a Poisson problem. This an adaptation of that problem. There is evidence that suggests that one in 200 carry a defective gene that is implicated in colon cancer. In a sample of 1000 individual, a. What is the probability that none of them would have the noted defective gene? b. What is the probability that between 4 and 7 (both inclusive) will carry the defective gene? c. What is the probability that at least 8 carry the defective gene? Notes: First establish that one can use Poisson distribution model, and use Excel or web-published probability tables.

Expert Solution

Solution: We are given that a defective gene follows the Poisson distribution with mean defective . We can approximate the Poisson distribution model to binomial distribution model as where n=1000, p=0.005.

Then the mean number of defectve items are

Now we can use poisson idtribution model with mean defective = 5

Let x be the number of defective gene's carried by any individual, then

We can use the Excel to find the mentioned probabilities:

a. What is the probability that none of them would have the noted defective gene?

Answer: We will use the Excel function =POISSON(0,5,FALSE) to find the probability that none of them would have the noted defective gene. The excel outputs are given below:

x

P(x)

0

0.006738

Where x is number of defective gene's carried by an individual and P(x) is the probability that none of them would have the noted defective gene.

b. What is the probability that between 4 and 7 (both inclusive) will carry the defective gene?

Answer: We will use the Excel function POISSON to find the probability that between 4 and 7 (both inclusive) will carry the defective gene. The excel outputs are given below:

Therefore the probability that between 4 and 7 (both inclusive) will carry the defective gene is 0.6016

c. What is the probability that at least 8 carry the defective gene?

Answer: We have to find here . It can also be written as . Therefore we will use the Excel function =1- POISSON(7,5,True) to find the probability that at least 8 carry the defective gene. The excel outputs are given below:

Therefore the probability that at least 8 carry the defective gene is 0.1334.

orchestra answered 2 years ago

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