Question

Instructions:

Answer ALL questions in the examination booklet. You are required to show your workings unless stated otherwise.

QUESTION 1

1. What is the lowest z-value for the lowest 5% of observations on the standard normal distribution?

  

2. If we know that the length of time it takes a university student to find a parking space in the university car park follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the Interquartile Range (IQR) for a randomly selected university student finding a parking space.

3. The daily sales of a retail store are normally distributed with a standard deviation of $500. If the probability that sales will be more than $10,000 in any one day is 60%, what are the mean daily sales?

4. A drinks machine dispenses coffee into cups. A sign on the machine indicates that each cup contains 100ml of coffee. The machine actually dispenses a mean amount of 105ml per cup and 10% of the cups contain less than the amount stated on the sign. Assuming that the amount of coffee dispenses into each cup is normally distributed, find the standard deviation of the amount of coffee dispensed per cup in ml.

5. Given the following table of values, find, showing ALL workings:

X=	0	1	2	3
P(X=x)	0.2	0.21	0.19	?

1. The missing probability.                     

Answer 1