a manufacture of halogen bulbs knows that 3% of the production of their 100W bulbs will dective

Tutors, sign in to answer this question.

Ryan S. | Mathematics and StatisticsMathematics and Statistics

This is an example of a binomial distribution. Each of the 12 bulbs in the carton is a "trial" with a 3% probability of being defective. We need to know how many ways we can have 5 bulbs be defective among 12. This is given by the combination function which can be written as n!/(k!(n-k)!) where n is the number of elements and k is the size of the combination. In this case n=12 and k=5.

(12*11*10*9*8*7*6*5*4*3*2*1)/(5*4*3*2*1*7*6*5*4*3*2*1)=792

So we have 792 combinations possible where there are 5 defective bulbs and 7 good bulbs. The probability for one of these is .03^5*.97^7. So the total probability is

792*.03^5*.97^7=0.00001555

By dividing 5 by .03, you find that it would take at least 166 bulbs to have 5 defective bulbs. Using a proportion to bring (5 out of 166 bulbs) down to (x out of twelve bulbs), you may find a probability of 0.36.

Please respond if this is not helpful. This answer was given to ignite some logical thought.

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Patty A.

Let Me Help Make Sense of All Those X's and Y's!!!

$12.25 per 15 min

View Profile >

Heidi L.

Creative Tutor for All Students and Learning Styles

$15 per 15 min

View Profile >

Tim K.

ACT, SAT, Math, Physics, Astronomy, & Electrical Engineering

$13.75 per 15 min

View Profile >

## Comments