2009 TEST PAPER
1. A `word' is made by writing the seven letters used to spell `EXAMPLE' in some order. Find how many different `words' are
possible in each of the following cases.
i. The first letter and the last letter are each “E”. 
ii. The two letters “E” are next to each other. 
iii. The two letters “E” are not next to each other. 
2. Janet and John wanted to compare their daily journey times to work, so they each kept a record of their journey times for a few
weeks. Janet's daily journey times, x minutes, for a period of 25 days, were summarised by = 2120 and = 180 044.
Calculate the mean and standard deviation of Janet's journey times. 
John's journey times had a mean of 79.7 minutes and a standard deviation of 6.22 minutes. Describe briefly, in everyday terms,
how Janet and ...view middle of the document...
i. Show that P(X = 4) = 1/3 , and draw up a table showing the probability distribution of X. 
ii. Hence find the value of E(X) . 
5. A bus serving a number of villages is due to arrive in a particular village at 10 o'clock. Past experience tells the people waiting
in the village for the bus that the probability of the service being cancelled on any day is 0.05, and that, when it runs, the
probability of the bus being late is 0.1. Draw a tree diagram to show this information. 
Using your tree diagram, find
i. the probability that the bus has not arrived in the village at 10 o'clock, 
ii. the conditional probability that the service has been cancelled, given that the bus has not arrived in the village at 10 o'clock 
6. The diagram shows the cumulative frequency graphs for the marks scored by the
candidates in an examination. The 2000 candidates each took two papers; the upper
curve shows the distribution of marks on paper 1 and the lower curve shows the
distribution on paper 2. The maximum mark on each paper was 100.
i. Use the diagram to estimate the median mark for each of paper I and paper 2, and
the interquartile range for paper 1. 
ii. State with a reason which of the two papers you think was the easier one. 
iii. The candidates' marks for the two papers could also be illustrated by means of a
pair of box-and whisker plots. Give two brief comments on any advantages or
disadvantages in using cumulative frequency graphs and box-and-whisker plots
to represent the data. 
7. Items from a production line are examined for any defects. The probability that any item will be found to be defective is 0.15,
independently of all other items.
i. A batch of 16 items is inspected. Calculate the probability that the number of defective items in the batch is
(a) exactly 2,  (b) at least 3. 
ii. A batch of 80 items is inspected. Use a normal approximation to a binomial distribution to find the probability that at least 8
items in the batch are defective.