Explore BrainMass

# Approximation to Binomial Distribution

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

If np ≥ 5 and nq ≥ 5 estimate P (fewer than 2) with n= 13 and p= 0.4 by using the normal distribution as an approximation to the binomial distribution if np < 5 or nq <5 then state that the normal approximation is not suitable.

Select the correct choice below and if necessary fill in the answer box to complete our choice.

P ( fewer than 2)=
The normal approximation is not suitable

© BrainMass Inc. brainmass.com October 2, 2022, 6:39 am ad1c9bdddf
https://brainmass.com/statistics/cumulative-distribution-function/approximation-binomial-distribution-582400

## SOLUTION This solution is FREE courtesy of BrainMass!

Now, np=13*0.4=5.2>5, and nq=13*(1-0.4)=7.8>5, so normal approximation is suitable

So mean= np=13*0.4=5.2 and sd=sqrt(13*0.4*0.6)=1.766

Since z=(x-mean)/sd

P( fewer than 2)=P(Z<(2-5.2)/1.766)=P(Z<-1.81)=0.0352 from standard normal table

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com October 2, 2022, 6:39 am ad1c9bdddf>
https://brainmass.com/statistics/cumulative-distribution-function/approximation-binomial-distribution-582400