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The Current Organ Donation System Is Not Working

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Submitted By zhijiaminghe886
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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”. [1] ii. The two letters “E” are next to each other. [1] iii. The two letters “E” are not next to each other. [2]

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. [3]

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 John's journey times compare. [2]

3. The random variable X is normally distributed, with mean and standard deviation each equal to a. It is given that
P(X < 3) = 0.25.

i. Find the value of a. [4] ii. Hence find P(X <12). [2]

4. A blue unbiased cubical die has one face marked 1, two faces marked 2 and three faces marked 3. A red unbiased cubical die has two faces marked 1, two faces marked 2 and two faces marked 3. The two dice are rolled together and X is the total score on the two dice. i. Show that P(X = 4) = 1/3 , and draw up a table showing the probability distribution of X. [6] ii. Hence find the value of E(X) . [2]

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.

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