Keep both tails of a call-duration difference and all handling fees

Independent call durations to City A are normal with mean 8 minutes and standard deviation 2.5 minutes; to City B, mean 10 and standard deviation 3.2.

(i) Find the probability that two random City A call durations in total differ from three times a third City A duration by more than 3 minutes.3 marks

Calls cost 22 cents per minute to A and 30 cents per minute to B, plus a 10 cent handling fee per call. Ann makes two calls to A and one to B.

(ii) Find her expected total cost.1 mark

(iii) Show that the probability her cost exceeds 8.50 dollars is 0.0870 to 3 significant figures.2 marks