A Level Mathematics Questionbanks



1. A tele-sales company are monitoring the length of time a sales call takes. They decide to model the length of a call (in minutes) as a continuous random variable Y, with probability density function shown below.

[pic]

a) Find the value of the constant a

[2]

b) Find, using this model, the probability a call takes more than 6 minutes

[4]

c) Give two reasons this model is unlikely to be realistic and sketch an improved model

[4]

2. A continuous random variable X has probability density function f(x), as defined below:

f(x) = [pic]

a) State the name of the distribution of X

[1]

b) State the mean of X

[1]

c) Find P(X>4 | X>3)

[4]

3. A continuous random variable X has probability density function f(x), as defined below

f(x) = [pic]

a) Sketch the graph of y=f(x)

[2]

b) Calculate the value of the constant k

[2]

c) State the mode of X

[1]

d) Calculate P(X>1)

[3]

4. For a Statistics project, a boy decides to model the length of time he spends on his homework

(in minutes) as a continuous random variable X with the probability density function shown below:

[pic]

a) Find the value of the constant k

[3]

The boy collected data to test this model over a eight week period (40 homework nights).

b) Use the model to calculate how many occasions he is expected to spend more than 70 minutes on his

homework over this period

[4]

The boy found that, over the eight week period, his time spent on homework varied between 10 minutes and 2½ hours, but on most nights he spent about an hour.

c) Comment on the suitability of the original model

[3]

d) Sketch the probability density function for an improved model

[2]

5. A continuous random variable X has probability density function f(x), as defined below

f(x) = [pic]

a) Sketch the graph of y=f(x)

[3]

b) State the mean of X

[1]

c) P(X ................
................

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