3. The probability that a person browsing the web clicks on a certain advertisem

Question

3. The probability that a person browsing the web clicks on a certain advertisement is 0.1% 170. The advertisement is viewed by one million web users a day who all behave independently. (a) What is the mean and standard deviation of the number of times the advertisement is clicked? (3pts) (b) What is the approximate probability of fewer than 950 clicks per day? (3 pts) (c) What is the approximate probability that the number of clicks falls between 960 and 1020? (3 pts) (d) Calculate the probability of more than 1020 clicks per day for the next 3 days. Assume the results between days are independent. (3 pts)

Explanation / Answer

a) mean =np =106*0.001 =1000

std deviation =(np(1-p))1/2 =(106*0.001*(1-0.001))1/2=31.607

b)

c)

d)

therefore due to independence probability that for next 3 days more than 1020 clicks =(0.2634)3 =0.0183

for normal distribution z score =(X-)/ here mean=       = 1000.000 std deviation   == 31.607

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