ZIMSEC A Level Statistics Paper 2 Past Papers

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Normal Distribution Poisson Distribution Correlation and Regressiontime seriesDescriptive Statistics Continuous Random Variables Confidence Intervals Probabilityhypothesis testing and chi-squaredHypothesis Testing

Explained questions

Which of the following is an advantage of using telephone interviews as a way of collecting data?
When selecting a number of objects from a set, which condition makes the selection a permutation rather than a combination?
What is the formula, in terms of n and r, for the number of permutations of r objects chosen from n distinct objects?
Whenever there is a power-cut, a school is equally likely (probability 1/3 each) to switch on one of its 3 generators A, B or C. The independent probabilities of a breakdown are 0.2 for A, 0.3 for B and 0.25 for C. For a randomly chosen day with a power-cut, what is the probability that there was a generator breakdown?
Using the same power-cut scenario (each generator equally likely to be switched on with probability 1/3; independent breakdown probabilities 0.2 for A, 0.3 for B, 0.25 for C), given that there was a generator breakdown, what is the probability that it was generator C?
An unbiased die with faces marked 1, 2, 2, 3, 3, 3 is rolled twice. If X is the total score on the two rolls, what is P(X = 4), as a fraction out of 36?
For a data set with D: 0, 5, 10, 15, 20, 25, 30, 35 and corresponding M: 90, 82, 56, 68, 58, 46, 30, 20, what is the product moment correlation coefficient r, to 3 decimal places?
For a data set with D: 0, 5, 10, 15, 20, 25, 30, 35 and corresponding M: 90, 82, 56, 68, 58, 46, 30, 20, the product moment correlation coefficient works out to r is approximately -0.957. Which statement best describes this correlation?
A random sample of 100 observations from a population gave $\sum(x - 50) = 123.5$ . What is the unbiased estimate of the population mean $\mu$ , to 3 decimal places?
A company receives on average 6 orders per day, following a Poisson distribution. What is the probability that no more than 2 orders will be received on a given day, to 3 decimal places?
Which statement correctly distinguishes a statistic from a parameter?
A sample of 10 toothpick lengths (cm): 4.99, 4.96, 5.00, 4.98, 5.01, 4.95, 4.96, 4.97, 4.99, 4.97 gives a sample mean of 4.978 cm and standard deviation of about 0.107 cm. Testing H0: mu = 5 against H1: mu is not equal to 5 at the 1% significance level gives a t-statistic of about -0.649, compared with a critical value of t(9) = 3.250. What is the conclusion?
A continuous random variable $X$ has probability density function $f(x) = \dfrac{x}{12}$ for $0 \le x < 3$ , $f(x) = k(x-8)$ for $3 \le x \le 8$ , and $f(x) = 0$ otherwise, where $k$ is a constant. Since the total area under $f$ must equal 1, what is the value of $k$ ?
A continuous random variable $X$ has probability density function $f(x) = \dfrac{x}{12}$ for $0 \le x < 3$ and $f(x) = -\dfrac{1}{20}(x-8)$ for $3 \le x \le 8$ (zero otherwise). What is $E(X)$ , correct to 2 decimal places?
A continuous random variable $X$ has probability density function $f(x) = \dfrac{x}{12}$ for $0 \le x < 3$ and $f(x) = -\dfrac{1}{20}(x-8)$ for $3 \le x \le 8$ (zero otherwise). What is the median of $X$ , correct to 2 decimal places?
A method of collecting statistical data involves obtaining information from every single member of a population, rather than from a sample of it. What is this method of data collection called?
In a survey of 100 athletes at a marathon, the amount of water taken, in litres, was recorded as: 0-0.5 litres by 8 athletes, 0.5-1.0 litres by 20 athletes, 1.0-1.5 litres by 29 athletes, 1.5-2.0 litres by 22 athletes, and 2.0-2.5 litres by 21 athletes. Using the midpoint of each class, what is the estimated mean amount of water taken, in litres?
In a survey of 100 athletes at a marathon, the amount of water taken, in litres, was recorded as: 0-0.5 litres by 8 athletes, 0.5-1.0 litres by 20 athletes, 1.0-1.5 litres by 29 athletes, 1.5-2.0 litres by 22 athletes, and 2.0-2.5 litres by 21 athletes. Using the midpoint of each class and a mean of 1.39 litres, what is the estimated standard deviation of the amount of water taken, correct to 3 decimal places?
The volume of dish washing liquid in satchets is normally distributed with mean 400 ml and standard deviation 45 ml, independent of the volume of fabric softener in bottles, which is normally distributed with mean 650 ml and standard deviation 50 ml. Let W be the total volume of 2 randomly chosen bottles of fabric softener minus the total volume of 4 randomly chosen satchets of dish washing liquid. What is the standard deviation of W, in ml (to 1 decimal place)?
A new detergent is made by mixing the contents of 1 satchet of dish washing liquid, mean volume 400 ml, with 2 bottles of fabric softener, mean volume 650 ml per bottle. What is the expected total volume of the new detergent, in ml?
A machine packs washing powder into packets with mean weight 2 kg. The weights are normally distributed, and 10% of packets weigh less than 1,95 kg. What is the standard deviation of the packet weights, in kg (to 3 decimal places)?
Packets of washing powder have weights normally distributed with mean 2 kg and standard deviation 0,039 kg. What proportion of packets weigh more than 2,10 kg? Give your answer to 3 decimal places or as a percentage.
A continuous random variable X has probability density function f(x) = (3/8)x^2 for 0 <= x <= 2. What is the cumulative distribution function F(x) for 0 <= x <= 2?
A continuous random variable X has cumulative distribution function F(x) = x^3/8 for 0 <= x <= 2. What is the median m of X? Give your answer to 3 decimal places.
A continuous random variable $X$ has probability density function $f(x) = 0.1x + k$ for $4 \leq x \leq 6$ , $f(x) = 0.3$ for $6 \leq x \leq 8$ , and $f(x) = 0$ otherwise. Find the value of the constant $k$ .
A continuous random variable $X$ has probability density function $f(x) = 0.1x - 0.3$ for $4 \leq x \leq 6$ , $f(x) = 0.3$ for $6 \leq x \leq 8$ , and $f(x) = 0$ otherwise. Find $P(5 \leq X \leq 7)$ .
Examination marks are displayed as below, with 1 alongside a leaf 3 standing for the mark 13 %.
The marks obtained by candidates in a mathematics examination are shown below, where a stem of 1 with a leaf of 3 means 13 %.

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