Question 5 (4 marks)

A call centre receives an average of 16 calls per hour according to a Poisson process. Calculate the following

probabilities, correct to 2 decimal places.

5.1 (2 marks) What is the probability that the call centre receives more than 10 but less than 12 calls in an

hour?

5.2 (2 marks) What is the probability that the call centre receives at least 1 call between 09:00 and 09:12?

Question 6 (3 marks)

6.1 (1 mark) Find the

P Z( 1.26)

where

Z N ~ 0,1 ( )

. Give you answer correct to 4 decimal places.

6.2 (1 mark) If

P Z k ( =) 0.791

, what is the value of k? Give your answer correct to 2 decimal places.

6.3 (1 mark) If

X N~ 80,25 ( )

, then the standardise value of x = 96 is a positive z-score. What is the value

of z? Only give the numerical answer to 1 decimal place. Do not include the sign in your answer.

Question 7 (4 marks)

It is assumed that the weight of the garbage collected per week by Pikitup is normally distributed with a mean

of 9 tonnes and a standard deviation of 2 tonnes.

7.1 (2 marks) What is the probability that Pikitup will collect less than 10.5 tonnes next week? Give your

answer correct to 4 decimal places.

7.2 (2 marks) What is the minimum weight of the heaviest 80% of garbage loads collected per week by

Pikitup? Give your answer correct to 2 decimal places.