it is given that 3% of electric blubs manufactured by a company are defective using poisson approximation find that a sample of 100 bulbs will contain no defective exactly one defective bulb
To find the probability of a specific number of events occurring in a Poisson distribution, we can use the formula:
P(x; λ) = (e^(-λ) * λ^x) / x!
where P(x; λ) represents the probability of x events occurring, λ is the average rate of events, e is the base of the natural logarithm (approximately 2.71828), and x! denotes the factorial of x.
In this case, we are given that 3% of electric bulbs manufactured by the company are defective. Therefore, the average rate of defective bulbs (λ) can be calculated as follows:
λ = (3/100) * 100 = 3
Now, to find the probability of exactly one defective bulb in a sample of 100 bulbs, we substitute x = 1 and λ = 3 into the Poisson formula:
P(1; 3) = (e^(-3) * 3^1) / 1!
Calculating this expression will give us the desired probability.