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 ................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- ordinary level mathematics study notes
- o level mathematics notes pdf
- a level mathematics revision
- a level mathematics past paper
- pure mathematics a level notes
- a level pure mathematics pdf
- a level mathematics textbook pdf
- a level mathematics pdf
- a level further mathematics pdf
- a level mathematics formula sheet
- a level mathematics notes
- a level mathematics questions