(a) A plane timetable states that a particular plane is due at 2pm but the actual arrival time isuniformly distributed between 1pm and 3pm.

(i) Calculate the probability that the plane arrives between 1:30pm and 2:10pm.

(ii) What arrival time can you be confident in stating that 95% of planes will arrive before?

iii)What percentage of flights arrive within one standard deviation of the mean arrival time?

(b) A cheese company produces a 500g packet of mozzarella cheese. If the packet weight is normally distributed with a mean of 505g and a standard deviation of 4g,

i) What percentage of packets are underweight ie. less than 500g?

(ii) What weight can the company guarantee its customers that 99% of mozzarella cheese packets weigh more than?

(iii) If the company wants to guarantee customers than only 1% of mozzarella packets of cheese are underweight, what mean weight should the company fill packets with, if the standard deviation remains unchanged at 4g?

(c) The number of employees absent from work at a large electronics manufacturing plant over a period of 106 days was given in Question 2 of Assignment 1. Decide whether the data appear to be approximately normally distributed by:

(i) Comparing data characteristics to theoretical properties.

(ii) Using PHStat2 to construct a normal probability plot.

(d) The owner of a self-service carwash has found that customers take an average of 12 minutes to wash and dry their cars. Assuming that the self-service times are exponentially distributed, what percentage of customers take less than 10 minutes?