Question

The rate of defects among cd players of a certain brand is 1.5%. use the poisson approximation to 19) the binomial distribution to find the probability that among 430 such cd players received by a store, there are exactly three defective cd players.

Answer 1

The solution for the problem using binomial distribution:
Given:
p = 1.5% or 0.015
n = 430
Mean = lambda = m = np = 430*0.015 = 6.45 According to Poisson distribution:
P(x) = e^-(np) *(np) ^x Where:
P is the probability of x
n is the sample size
e is the exponential constant
P(3)= e^-(430*1.5/100) * (430*1.5/100)^3
P(3)= 0.00158* 268.3336125
P(3) = 0.4240%

Answer 2

The poison distribution can be used to approximate the binomial distribution when the sample size n is large. This is then calculated using the formula P(X) = e^-(np) *(np)^x substituting X= 3 P(3)= e^-(430*1.5/100) * (430*1.5/100)^3 P(3)= 0.00158*268.3 P(3) = 0.42 P(3) = 0.0042% P= probability of X occurring given n and p n= sample size p= true probability e= exponential constant ~2.718 X=number of sample successes