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.

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

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%