Q2 At the tennis club social a raffle was run with first prize of $100 and four

Q2 At the tennis club social a raffle was run with first prize of $100 and four (4) second prizes of a bottle of wine purchased for $9 each. Fifty tickets were sold at $5 each.
(a) Suppose you bought one ticket. Set up a table for the probability distribution for the random variable X = Value of prize you will win.
x
P(X = x) [3]
(b) What is the expected value of X and what does it mean in this context? [2]
Q3 According to Wikipedia in August 2010 Windows XP had a 48.5% share of web client operating systems. Of 20 students in a statistics class:
(a) What is the probability that none of the 20 students have Windows XP?
[2]
(b) What is the probability that at least 15 students use Windows XP? [2]
(c) What are the expected number and standard deviation of the number of students (of the 20) who use Windows XP? [2]
(d) What assumption(s) are necessary so that you can answer (a) (b) and (c) ?
[2]
Q4 The local health board operates a fleet of cars. Based on past information for the cars used the distance traveled by a car in a day averages 170 km with a standard deviation of 40 km. Assuming a normal distribution of distances:
(a) What proportion of cars used in any day travel less than 100 km? [3]
(b) What daily distance would be traveled by the 10% of cars that travel the greatest distance? [3]
(c) A car is booked out for 5 days. What is the probability that the total distance traveled is more than 1100 km?
(Material for this question covered in CAST 6.1.6). [4]
Q5 A plumbing and drainage business offers a 24 hour callout service. They operate two trucks neither of which is very reliable. One truck is available for use 90% of the time and the other is available for use only 80% of the time.
(a) What is the probability that on a particular day neither truck is available?
[2]
(b) What is the probability that on a particular day at least one truck is available?
[1]
(c) What did you assume about the trucks to answer (a) and (b) ?
[1]
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