有冇可以幫我呀..?
1. The number of hits on a website is recorded.Over a long period of time the
mean number if hits per hour is 6.9.
i) explain briefly why the number of hits per unit time could be modelled by a
Poission distribution,
ii) Assuming a Poission model, calculate the probability that the websites has
(A) exactly 6 hits in an hour,
(B) exactly 3 hits in each of two successive 30-minute intervals
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.
i) State the condition required for X to be binomially distributed.
ii) Hence find the probability that a randomly selected monitor screen has
(A) exactly one faulty pixel,
(B) at least two faulty pixels.
iii) A retailer orders a batch of 5 monitor screens from the manufacturer. (The batch may be regarded as a random sample)
(A) Find the probability that exactly one of the five monitor screens has at
least two faulty pixels.
(B) Find the probability that there are at most 10 faulty pixels in total in the
batch,
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?