Question

A manufacturer has 100 bottles in stock of which 8% are deffective (based on past experience). A random sample of 5 bottles are selected and shipped to a factory.

Let:

X= the number of deffective bottles shipped

Determine the probability distribution of X and the E(X) and Standard Deviation of X.

Answer 1

A manufacturer has 100 bottles in stock of which 8% are deffective (based on past experience). A random sample of 5 bottles are selected and shipped to a factory.

Let: X= the number of deffective bottles shipped.

Here we can say that the random variable is to follow binomial distribution. Because the condition of Binomial Distribution i.e.

1) The number of observations is fixed that is number of bottle selected and shipped to a factory ,n= 5.

2) Each trial is independent.

3) The probability of success that is bottle is defective p = 8%= 0.08 is same for each trial.

Therefore the given random variable is x is follow the Binomial Distribution with (n=5, p= 0.08).

The mean and variance of binomial distribution is .

E( X )= np= 5*0.08=0.4

V( X) = npq= 5*0.08*0.92= 0.368

Standard deviation of X= √V ( X) =√ (0.368)= 0.6066