Question

Question #e49ee

Answer 1

p = 0.3, n= 12, let x = The number of accidents to 18 year old drivers within one year of taking license;
Required Prob. = 0.49071.

Explanation:

X follows binomial distribution with n= 12 and p = 0.3
general p.d.f. is f ( x) = `n C _x` `p^x` `q^ (n-x)` , x = 0,1,2...n and q = 1 - p.
Required Pr{ X `<=` 3} = Pr { x = 0, 1, 2, 3}
= Pr {X = 0} + Pr{X = 1} + Pr { X = 2} + Pr {X = 3} = `12 C _0` `(0.7)^12` + `12 C _1` 0.3`(0.7)^11` + `12C_2` `(0.3) ^2` `(0.7)^10` + `12 C _3` `(0.3)^3` `(0.7)^9`
= 0.01384 + 0.07118 + 0. 16779 + 0.23790 =0.49071

Answer 2

Refer explanation section

Explanation:

Following Binomial Distribution the answer is `P_(x<3)=0.4919`
Following Poisson Distribution the answer is `P_(x<3)=0.51517`
Following Normal Distribution the answer is `P_(x<3)=0.352`

I am sorry I have wrongly totaled the probability values.
I have redone the problem using the three distributions.
I have enclosed my work in a pdf file form.

I am unable to get the answer that you have given 0.3327.

May I know in which area the problem appears in your book.

This is the link to the pdf File

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