It is known from past experience that in a certain factory 3% of products are defective. a sample of 100 items are taken at random. find the probability that exactly 5 products are defective.
Answers
Given:
In a certain factory 3% of products are defective.
A sample of 100 items are taken at random.
To find:
Find the probability that exactly 5 products are defective.
Solution:
From given, we have,
n = total number of items/samples = 100
p = Probability of defective = 3/100 = 0.03
x = No. of defective items = 5
Now, we will find λ which is the parameter of Poisson distribution.
λ = n × p = 100 × 0.03 = 3
Now as we know,
P (X) = ( 3⁵ × e ^-3 ) / 5!
= (243 × 0.04978) / 120
= 0.1008
Therefore, the probability that exactly 5 products are defective is 0.1008.
Given : in a certain factory 3% of products are defective. a sample of 100 items are taken at random
To find : the probability that exactly 5 products are defective
Solution:
a certain factory 3% of products are defective
=> Probability of Defective p = 3/100
Probability of non-defective q = 1 - 3/100 = 97/100
Sample of 100 items => n = 100
Exactly 5 Defectives => x = 5
P(x) = ⁿCₓpˣqⁿ⁻ˣ
=> P(5) = ¹⁰⁰C₅(3/100)⁵(97/100)⁹⁵
= 0.1013
probability that exactly 5 products are defective = 0.1013
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