A. The client needs to decide if he should invest on the stocks of a food delivery company, called Pippo. The annual profit per 100 invested for Pippo has been estimated that will follow the probability distribution in the following table:

Pippo
Profit per 100	Probabilities
160	0.10
120	0.25
700	0.20
200	0.15
-300	0.20
-800	0.10

A second stock, of the rival food delivery company called Paperino has the following estimated profit per 100 invested and associated probabilities:

Paperino
Profit	Probabilities
85	0.10
60	0.25
45	0.20
25	0.15
15	0.20
10	0.10

The client is also investigating the possibility to invest in stocks related to delivery companies and wants to estimate the average rate of return for the stocks of a delivery companies. It has been estimated that standard deviation for delivery companies stocks is approximately 20%. The client wants to estimate a 95% confidence interval for the average rate of return that must extend no more than 2% on each side of the sample mean.

The client will conduct this analysis only if the sample observations needed are less than 100. Can you suggest if he needs more or less than 100 observations? [5 marks]