Question

The probability that a part produced by a certain? factory's assembly line will be defective is 0.035. Find the probabilities that in a run of 44 ?items, the following results are obtained. ?(a) Exactly 3 defective items ?(b) No defective items ?(c) At least 1 defective item

Answer 1

Answer:

Step-by-step explanation:

P\left ( defective item\right )=0.035

Using binomial distribution

Where p= probability of success

q=probability of failure

Here p=0.035

q=1-0.035=0.965

$^nC_{r}P^{r}q^{n-r}$

(i)for exactly 3 defective items i.e. r=3

P$\left ( r=3\right )$=$^{44}C_{3}$$\left ( 0.035\right )^{3}\left ( 0.965\right )^{44-3}$

P=$\frac{44!}{41!3!}\times \left ( 0.035\right )^3\left ( 0.965\right )^{41}$

P=0.1317

(ii)No defective item i.e. r=0

P$\left ( r=0\right )$=$^{44}C_{0}$$\left ( 0.035\right )^{0}$$\left ( 0.965\right )^{44-0}$

P=$\frac{44!}{44!0!}\times \left ( 0.035\right )^0\left ( 0.965\right )^{44}$

P=0.2085

(iii)At least 1 defective item

P=1-P(zero defective item)

P=1-$^{44}C_{1}\left ( 0.035\right )^{1}\left ( 0.965\right )^{44-1}$

P=1-$\frac{44!}{43!1!}\times \left ( 0.035\right )^1$$\left ( 0.965\right )^{43}$

P=0.6671