a. On average 12 people every half hour check in at Counter A at the Qantas domestic terminal at Terminal 2 at Sydney airport. The people arrive at the counter randomly and independently. 
b. 
i) Identify the type of probability distribution represented by this problem and write down the value(s) of the parameter(s). 
ii) 
iii) Calculate the probability of more than 13 people checking in at Counter A in the next half hour. (4 marks) 
iv) 
iii) Calculate the probability of exactly 5 people checking in at Counter A in the next 15 minutes. 

B Let X be the number of cars a mechanic repairs on a given day. The distribution of X follows. 
Num cars X 2 3 4 5 6 
Probability 0.10 0.15 0.35 0.23 0.17 

Calculate the mean and standard deviation for this probability distribution 
Question 2 
Marking Criteria 
Marks will be awarded for: 
• the correct answers and appropriate detailed working including the relevant formula; 
• the correct use of Excel where appropriate; 
• a sentence which answers each question asked. 

An office supply company conducted a survey before marketing a new paper shredder designed for home use. In the survey, 75% of the people who used the shredder were satisfied with it so the company decided to market it. Assume that 75% of all people who will use the new shredder will be satisfied 
I. Find the probability that for a random sample of 20 customers who purchased the new shredder, exactly 16 of these will be satisfied with it. 
II. Find the probability that for a random sample of 20 customers who purchased the new shredder, less than 14 of these will be satisfied with it. 

III. Find the expected number of dissatisfied customers in a sample of 50 customers who purchased the new shredder. 

IV. Find the probability that for a random sample of 100 customers who purchased the new shredder, exactly 75 of these will be satisfied with it. 

V. Find the probability that for a random sample of 150 customers who purchased the new shredder, more than 95 will be satisfied with it. 

Hint: Use the appropriate statistical tables to determine the probabilities in parts a. and b. and use the appropriate Excel statistical function to determine the probabilities in parts d. and e. Include the Excel formula used (in d. and e.) when giving your answer. 

Question 3 
In a drawer there are 30 ribbons, 16 are blue and the rest are red. Two ribbons are selected at random from the drawer, without replacement. 

? Draw a probability tree diagram to represent this problem. Label the end of each branch with the simple events and include the probabilities along each branch of the tree. 

? If two ribbons are drawn at random what is the probability of selecting a pair of matching ribbons (two ribbons the same colour)?