# Question #e49ee

Sep 17, 2015

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 $\le$ 3} = Pr { x = 0, 1, 2, 3}
= Pr {X = 0} + Pr{X = 1} + Pr { X = 2} + Pr {X = 3} = $12 {C}_{0}$${\left(0.7\right)}^{12}$ + $12 {C}_{1}$ 0.3${\left(0.7\right)}^{11}$ + $12 {C}_{2}$ ${\left(0.3\right)}^{2}$${\left(0.7\right)}^{10}$ + $12 {C}_{3}$ ${\left(0.3\right)}^{3}$ ${\left(0.7\right)}^{9}$
= 0.01384 + 0.07118 + 0. 16779 + 0.23790 =0.49071

Sep 17, 2015

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