Question

A fair 10-sided die is rolled 122 times. Consider the event A  =  {the face 6 comes up at most 2 times}.

(a)	Find the normal approximation for P(A) without the continuity correction.

(b)	Find the normal approximation for P(A) with the continuity correction.

(c)	Find the Poisson approximation for P(A).

Answer 1

Hi,

Given that 10sided fair sie rolled 122 times

Then n= 122

Probability of face 6 comes up = 1/10

p= 1/10=0.1

Normal approximation→

Mean( u)= 122*0.1=12.2

Standard deviation (s)=√(npq)=3.313608

(a)

Probability of face come up at most 2 time

=Prob(x≤2)

=Prob(z≤(2-12.2)/3.313608)

=Prob(z<-3.078216)

=0.0010

(b)

Probability of face come up at most 2 time

=Prob(x≤2)

=Prob(x<2.5).        (Continuity correction factor)

Z score= (x-u)/s=(2.5-12.2)/3.313608=-2.9273

=Prob(z<-2.9273)

=0.0017

Que(c)

Lamda= n*p= 122*0.1= 12.2

P(x=x)= exp(-lamda)*(lamda)^x/x!

=Prob(x≤2)

=0.00037

Thanks!

Stay safe!

Thanks!

Stay sa