Question

4. Of all the registered automobiles in a certain state, 10% violate the state emissions standard. Twelve automobiles are selected at random to undergo an emissions test. Answer the following questions by defining the associated random variables. i) Find the probability that exactly three of them violate the standards. ii) Find the probably that fewer than three of them violate the standards. iii) Find the probably that none of them violate the standards. iv) How many of them do you expect to violate the standard on average?

Answer 1

Hello

In the given binomial distribution,

p	10.00%
n	12

Using the below formula:

n-1 P(X =r) = (?)?" p" (1 – p)?

We can calculate the probability distribution:

x	P(x)
0	0.2824
1	0.3766
2	0.2301
3	0.0852
4	0.0213
5	0.0038
6	0.0005
7	0.0000
8	0.0000
9	0.0000
10	0.0000
11	0.0000
12	0.0000

Hence,

(a)

P(X = 3) = 0.0852

(b)

P(X < 3) = 0.8891

(c)

P(X = 0) = 0.2824

(d)

Expected No. of violations = 10%*12 = 1.2 violations

Thanks!

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