Question

Q1.The probability of getting an item
defective is 0.005. Find the probability
that exactly 3 items in a sample of
200 are defective.
1
(Given e
= 0.3679)
0.5131
0.7131
0.06131
0.4131​

Answer 1

Step-by-step explanation:

SOLUTION

TO CHOOSE THE CORRECT OPTION

The probability of getting an item defective is 0.005. Find the probability that exactly 3 items in a sample of 200 are defective.

( Given

${e}^{ - 1}$

= 0.3679 )

0.5131

0.7131

0.06131

0.4131

CONCEPT TO BE IMPLEMENTED

POISSON DISTRIBUTION :

X is a poisson random variable with parameter μ then

$\displaystyle \sf{P(X = r) = {e}^{ - \mu}. \frac{ { \mu}^{r} }{r \: !} }$

Where μ > 0 and r = 1 , 2 , 3 , ....

EVALUATION

Here it is given that the probability of getting an item defective is 0.005

Thus p = 0.005

We have to find the probability that exactly 3 items in a sample of 200 are defective

Thus n = Sample size = 200

Since sample size is large

So application of Poisson distribution is recommended

Mean = μ = np = 200 × 0.005 = 1

Also r = 3

Hence the required probability

= P( X = 3 )

$\displaystyle \sf{ = {e}^{ - 1}. \frac{ {1}^{3} }{3 \: !} }$

$\displaystyle \sf{ = \frac{ {e}^{ - 1} }{6} }$

$\displaystyle \sf{ = \frac{ 0.3679 }{6} }$

= 0.06131

FINAL ANSWER

Hence the correct option is 0.06131.

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