Question

Find the probability that at least 5 defective bolts will be found in a box of 200 bolts. If it is known that
2% of such bolts are expected to be defective (Given: e–4 = 0.0183)

a. 0.4717

b. 0.3717

c. 0.3017

d. None of these​

Answer 1

Answer:

Step-by-step explanation:

The Poisson Distribution is

P(X=x) = e⁻λ * λˣ / x!

Let X be the defective bolt.

p = 2/100 = 0.02

n = 200

λ = np = 200 * 0.02 = 4

Since we need to find Probability of at least 5 defective bolts (5 or more than 5)  i.e. P(X≥5)

P(X≥5) = 1 - P(X≤4)

            = 1 - [P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)]

P(X=0) = e⁻⁴ * 4⁰/0! = 0.0183 * 1 = 0.0183

P(X=1) = e⁻⁴ * 4¹/1! = 4*0.0183 = 0.0732

P(X=2) =e⁻⁴ * 4²/2! = 8 * 0.0183 = 0.1464

P(X=3) = e⁻⁴ * 4³/3! = 0.1952

P(X=4) = e⁻⁴ * 4⁴/4!  = 0.1952

P(X≥5) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)]

            = 1 - [0.0183+ 0.0732 +0.1464+0.1952 +0.1952] =  1 - 0.6283 = 0.3717.