2. A manufacturer produces computer monitor screens in which the picture is
composed of 780 000 pixels. On average 1 in 500 000 of these pixels is faulty.
Let X represent the number of faulty pixels in one monitor screen.
A retailer orders a batch of 5 monitor screens from the manufacturer. (The batch may be regarded as a random sample)
iv) The manufacturer wishes to improve quality so that 90% of the monitor screens have no faulty pixels at all. To what value must the manufacturer reduce the probability of a piexl being faulty in order to achieve this?
I don't understand what this question is asking, is it 90% of the screens in the batch that he wants to reduce the probability of?
I tried doing the following:
X~Po(1.56)
P(X=0) = 0.21
90% of 5 = 4.5 so 4.5 screens must have no faulty pixels
(0.210^4.5) * (0.790^0.5) = 7.9x10^-4
However this doesnt seem right, since now the probability that there can be a faulty pixel per screen is bigger than before? where have i gone wrong?