Edexcel A Level Maths S2 · Statistics 2 June 2015 question paper 6684

In a survey it is found that barn owls occur randomly at a rate of 9 per 1000 km².

Find the probability that in a randomly selected area of 1000 km² there are at least 10 barn owls.

Find the probability that in a randomly selected area of 200 km² there are exactly 2 barn owls.

Using a suitable approximation, find the probability that in a randomly selected area of 50000 km² there are at least 470 barn owls.

The proportion of houses in Radville which are unable to receive digital radio is 25%. In a survey of a random sample of 30 houses taken from Radville, the number, X, of houses which are unable to receive digital radio is recorded.

Find P(5 ≤ X 11)

A radio company claims that a new transmitter set up in Radville will reduce the proportion of houses which are unable to receive digital radio. After the new transmitter has been set up, a random sample of 15 houses is taken, of which 1 house is unable to receive digital radio.

Test, at the 10% level of significance, the radio company’s claim. State your hypotheses clearly.

A random variable X has probability density function given by

where k is a constant.

Write down the mode of X.

Specify fully the cumulative distribution function F(x).

Find the upper quartile of X.

The continuous random variable L represents the error, in metres, made when a machine cuts poles to a target length. The distribution of L is a continuous uniform distribution over the interval [0, 0.5]

Find P(L < 0.4).

Write down E(L).

Calculate Var(L).

A random sample of 30 poles cut by this machine is taken.

Find the probability that fewer than 4 poles have an error of more than 0.4 metres from the target length.

When a new machine cuts poles to a target length, the error, X metres, is modelled by the cumulative distribution function F(x) where

Using this model, find P(X 0.4)

A random sample of 100 poles cut by this new machine is taken.

Using a suitable approximation, find the probability that at least 8 of these poles have an error of more than 0.4 metres.

Liftsforall claims that the lift they maintain in a block of flats breaks down at random at a mean rate of 4 times per month. To test this, the number of times the lift breaks down in a month is recorded.

Using a 5% level of significance, find the critical region for a two-tailed test of the null hypothesis that ‘the mean rate at which the lift breaks down is 4 times per month’. The probability of rejection in each of the tails should be as close to 2.5% as possible.

Over a randomly selected 1 month period the lift broke down 3 times.

Test, at the 5% level of significance, whether Liftsforall ’s claim is correct. State your hypotheses clearly.

State the actual significance level of this test.

The residents in the block of flats have a maintenance contract with Liftsforall. The residents pay Liftsforall £500 for every quarter (3 months) in which there are at most 3 breakdowns. If there are 4 or more breakdowns in a quarter then the residents do not pay for that quarter. Liftsforall installs a new lift in the block of flats. Given that the new lift breaks down at a mean rate of 2 times per month,

find the probability that the residents do not pay more than £500 to Liftsforall in the next year.

A continuous random variable X has probability density function f(x) where

where k and n are positive integers.

Find k in terms of n.

Find E(X) in terms of n.

Find E(X²) in terms of n.

Given that n = 2

find Var(3 X).

A bag contains a large number of 10p, 20p and 50p coins in the ratio 1: 2: 2 A random sample of 3 coins is taken from the bag. Find the sampling distribution of the median of these samples.