Mathematics Questions

Question 1

A web publisher provides information on travelling to China. Access to the website is free but revenues are generated by selling ads that are posted on the website. In the following month, the website has committed to display ads to 650,000 viewers, i.e., 650,000 impressions. Based on data from previous months the traffic to the website is estimated to be normally distributed with a mean of 850,000 viewers and a standard deviation of 150,000. (You need to use a normal table or Excel for this question.)

a) What is the probability that the web publisher will be able to deliver the promised impressions?

b) How many impressions should the web publisher have taken on, to be able to guarantee a 95% service level?

Question 2

Which one of the following statements is true?

a) If we know the mean of the normal distribution we know its shape

b) In the normal distribution, the mean, median, mode, and standard deviation are all at the same position on the horizontal axis since the distribution is symmetric.

c) Normal distribution that is wide has a high standard deviation

Question 3

ABC Fund Managers Plc claims that the monthly returns to their high-income tracker fund exceed the index return by 0.003 (i.e. 0.3%). Over a one-year period the average amount by which the tracker fund exceeds the index is 0.001. The standard deviation of the difference is calculated as 0.004 over this period. Explain how you can test the claim using a one-tailed hypothesis test.