Binomial Distribution Real Life Examples
In this class, We discuss Binomial Distribution Real Life Examples.
The reader should have prior knowledge of Binomial Distribution. Click Here.
Example 1:
Previously collected data says thirty thousand coronavirus tests are conducted.
Out of thirty thousand, eighteen thousand are positive.
Today we are doing ten tests. What is the probability that atmost eight patients have the coronavirus?
Solution:
First, think, is the given question applicable to binomial distribution?.
Previously collected data provide the probability of getting the coronavirus.
Probability = 18000/ 30000 = 0.6
Important: each test is independent of the other.
The test result is either positive or negative. so bernoulli experiment.
n = 10 from the question.
p = 0.6
x = at least 8
We need to find the cumulative sum of the probabilities for random variable X = 0, 1, 2, 3, 4,5, 6, 7, 8.
P(X lt= 8) = Σ all x lt=8 (f(x; n, p))
The sum of all the probability values in the distribution is equal to one.
So for ease of calculation we do P(X lt= 8) = 1 - (P(X = 9) + P(X = 10)).
= 1 - ((10C9 (0.6)^9 (0.4)^1) + (10C10 (0.6)^10 (0.4)^0))
Example 2:
The probability of a man hitting a target is 1/3.
1) If he fires five times, What is the probability of hitting the target atleast twice.
2) How many times must he fire so that the probability of hitting the target atleast once is more than 90%.
Solution:
1) P(Xgt= 2) = 1 - P(Xlt2)
1 - [5C0 (1/3)^0 (2/3)^5 + 5C1 (1/3)^1 (2/3)^4]
= 0.5391
2) P(X gt=1) gt 0.9
1 - P(X=0) gt 0.9
1 - nC0 (1/3)^0 (2/3)^9 gt 0.9
1 - (2/3)^ lt 0.9
Trail and error n = 6
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10 июл 2022
