Probability - Binomial Distribution

Question

It has been found that 80% of all printers used operate correctly at the time of installation. A seller sells 10 units during a month.

1)find the prob.that at least 9 of the printers operate correctly at the time of installation.

2)Consider 5 months in which 10 units are sold per month. What is the prob.that at least 9 units operate correctly in each of the 5 months

For 1st part :

Let p(o)=probability that a given printers operates correctly

So we have to find p(o>=9) here.

I understand that for the first part we have use Binomial distribution

But how do we solve the 2nd part?

Answer 1

Hello -

For step one I would use the binomial table to add the results for 9 successes and 10 successes out of 10 for p=.8

P(9/10) = .268 + P(10/10)= .107

.268+.107= .375

Then for part 2 use the answer for part a as your monthly probability

In other words, the probability of 9 of 10 printers working each month is 0.375

Therefore the probability of 9 of 10 or better working 5 months in a row is...

(0.375)(0.375)(0.375)(0.375)(0.375) = (0.375)^5 = 0.0074