Answer to Question #139966 in Statistics and Probability for Draisma1

Question

b. A stamping device for University of Lusaka reception is not working properly and producing 15% defectives. The defective and no defective stampings proceed from the machine on a random manner.
i. If 4 stampings are randomly collected, find the probability that 2 of them are defective. [4 Marks]
ii. Find the mean, variance and standard deviation?

Answer 1

i.Let $X=$ the number of found defective numbers: $X\sim Bin(n, p)$

$$P(X=x)=\dbinom{n}{x}p^x(1-p)^{n-x}$$

Given $p=0.15, n=4$

$$P(X=2)=\dbinom{4}{2}0.15^2(1-0.15)^{4-2}=$$

$$=\dfrac{4!}{2!(4-2)!}0.15^20.85^2=0.0975375$$

ii.

$$mean=\mu=np=4(0.15)=0.6$$

$$variance=\sigma^2=np(1-p)=4(0.15)(1-0.15)=0.51$$

$$standard \ deviation=\sigma=\sqrt{\sigma^2}=\sqrt{0.51}\approx0.711443$$