Sampling and estimation — AS & A Level Mathematics (9709) questions by topic
Finding a confidence interval for a train journey's mean time from a sample, estimating a population proportion who own a car from a survey, judging whether a calculator-generated random-number method gives a genuine simple random sample, and constructing a confidence interval from summarised sample data are typical of the 28 sampling and estimation questions from 2023 to 2025, worth 3 to 9 marks.
Find and calculate dominate the command words, with explain, state and test used to justify a sampling method or interpret an interval's meaning. Because an unbiased estimate depends on using the correct sample variance formula, submit your interval calculations for instant marking, so a wrongly adjusted variance or a misapplied confidence-level multiplier is caught before the whole interval is built on it.
May–June 2025, Paper 62
The height of a certain species of plant is denoted by H cm. The heights of a random sample of 100 plants were measured, and the following results were found. - The mean, h-bar,…
Answer this question and get it marked →A biased spinner has four sides. Each side is of a different colour: yellow, red, green or black. The probability, p, that the spinner will land on red is unknown. The spinner was…
Answer this question and get it marked →May–June 2025, Paper 63
A machine dispenses coffee into cups. The volume, V cm^3, of coffee in a cup was measured for a random sample of 150 cups. The results were summarised as follows. sum v = 46350…
Answer this question and get it marked →Emma needs to choose one person at random from three people, P, Q and R. She plans to throw two fair coins and note the number, n, of heads. If n is 0, she will choose P. If n is…
Answer this question and get it marked →May–June 2025, Paper 65
A random sample of 200 values of a random variable X gives the following results. n = 200, sum(x - 2) = 60, sum((x - 2)^2) = 20 Find a 95% confidence interval for the population…
Answer this question and get it marked →Maroulla's calculator can generate random numbers between 0.000 and 0.999 inclusive, correct to 3 significant figures. She plans to use her calculator to choose a sample of…
Answer this question and get it marked →May–June 2024, Paper 61
The time taken in minutes for a certain daily train journey has a normal distribution with standard deviation 5.8. For a random sample of 20 days the journey times were noted and…
Answer this question and get it marked →A random sample of 8 boxes of cereal from a certain supplier was taken. Each box was weighed and the masses in grams were as follows. 261 249 259 252 255 256 258 254 Find unbiased…
Answer this question and get it marked →May–June 2024, Paper 62
Henri wants to choose a random sample from the 804 students at his college. He numbers the students from 1 to 804 and then uses random numbers generated by his calculator. The…
Answer this question and get it marked →A student wishes to estimate the proportion, p, of students at her college who have exactly one brother. She surveys a random sample of 50 students at her college and finds that…
Answer this question and get it marked →May–June 2024, Paper 63
The widths, w cm, of a random sample of 150 leaves of a certain kind were measured. The sample mean of w was found to be 3.12 cm. Using this sample, an approximate 95% confidence…
Answer this question and get it marked →The numbers of green sweets in 200 randomly chosen packets of Frutos are summarised in the table. Number of green sweets 0 1 2 3 3 --- --- --- --- --- --- Number of packets 32 50…
Answer this question and get it marked →October–November 2024, Paper 61
The heights of a certain species of deer are known to have standard deviation 0.35 m. A zoologist takes a random sample of 150 of these deer and finds that the mean height of the…
Answer this question and get it marked →The times, T minutes, taken by a random sample of 75 students to complete a test were noted. The results were summarised by Sum t = 230 and Sum t^2 = 930. (a) Calculate unbiased…
Answer this question and get it marked →October–November 2024, Paper 62
The lengths of a random sample of 50 roads in a certain region were measured. Using the results, a 95% confidence interval for the mean length, in metres, of all roads in this…
Answer this question and get it marked →October–November 2024, Paper 63
The heights of a certain species of deer are known to have standard deviation 0.35 m. A zoologist takes a random sample of 150 of these deer and finds that the mean height of the…
Answer this question and get it marked →The times, T minutes, taken by a random sample of 75 students to complete a test were noted. The results were summarised by Sum(t) = 230 and Sum(t^2) = 930. Calculate unbiased…
Answer this question and get it marked →May–June 2023, Paper 61
A certain train journey takes place every day throughout the year. The time taken, in minutes, for the journey is normally distributed with variance 11.2. The mean time for a…
Answer this question and get it marked →A sample of 5 randomly selected values of a variable X is as follows: 1 2 6 1 a where a 0. Given that an unbiased estimate of the variance of X calculated from this sample is…
Answer this question and get it marked →May–June 2023, Paper 62
In a survey of 200 randomly chosen students from a certain college, 23% of the students said that they owned a car. Calculate an approximate 93% confidence interval for the…
Answer this question and get it marked →The masses, in kilograms, of newborn babies in country A are represented by the random variable X, with mean μ and variance σ². The masses of a random sample of 500 newborn babies…
Answer this question and get it marked →May–June 2023, Paper 63
A club has 264 members, numbered from 1 to 264. Donash wants to choose a random sample of members for a survey. In order to choose the members for the sample he uses his…
Answer this question and get it marked →In a random sample of 100 students at Luciana's college, x students said that they liked exams. Luciana used this result to find an approximate 90% confidence interval for the…
Answer this question and get it marked →Last year the mean time for pizza deliveries from Pete's Pizza Pit was 32.4 minutes. This year the time, t minutes, for pizza deliveries from Pete's Pizza Pit was recorded for a…
Answer this question and get it marked →October–November 2023, Paper 61
A random variable X has the distribution N(410, 400). Find the probability that the mean of a random sample of 36 values of X is less than 405.
Answer this question and get it marked →In a survey of 300 randomly chosen adults in Rickton, 134 said that they exercised regularly. This information was used to calculate an alpha% confidence interval for the…
Answer this question and get it marked →October–November 2023, Paper 62
The length, in minutes, of mathematics lectures at a certain college has mean μ and standard deviation 8.3. The total length of a random sample of 85 lectures was 4590 minutes.…
Answer this question and get it marked →October–November 2023, Paper 63
In a survey of 300 randomly chosen adults in Rickton, 134 said that they exercised regularly. This information was used to calculate an alpha% confidence interval for the…
Answer this question and get it marked →Other AS & A Level Mathematics topics
- Differentiation (95)
- Algebra, logarithmic and exponential functions (87)
- Trigonometry (57)
- Series (37)
- Integration (33)
- Kinematics (33)
- The normal distribution (32)
- Energy, work and power (31)
- The Poisson distribution (31)
- Complex numbers (28)
- Permutations and combinations (27)
- Representation of data (23)