The normal distribution — AS & A Level Mathematics (9709) questions by topic
Combining independent normal distributions for small and large bags' masses, finding the probability that a sample mean falls below a stated value, and using a normal approximation to a binomial election-sample scenario span the 32 normal distribution questions from 2023 to 2025, worth 3 to 12 marks.
Find and calculate top the command words, with explain and test used where a continuity correction or approximation condition must be justified. Because standardising the wrong mean or variance derails an entire probability calculation, submit your working for instant marking to catch a mismatched standard deviation or an omitted continuity correction at the precise line it occurs, before the final probability is even reached.
May–June 2025, Paper 51
The masses of the bags of rice made by a company are normally distributed with mean mu kg and standard deviation 0.14 kg. The probability that the mass of a randomly chosen bag of…
Answer this question and get it marked →Every Saturday, a particular community holds a 'Puzzle' event to raise money for a new Leisure Centre. Competitors attempt to solve a puzzle as quickly as possible. Last Saturday,…
Answer this question and get it marked →May–June 2025, Paper 52
In Millford, 70% of the residents own a bicycle. A random sample of 160 residents is selected. Use a suitable approximation to find the probability that more than 120 of these…
Answer this question and get it marked →Kestrels are birds whose adult wingspans are normally distributed with mean 74.8 cm and standard deviation 3.2 cm. A random sample of 120 adult kestrels is selected. How many of…
Answer this question and get it marked →May–June 2025, Paper 53
A company sells bags of pasta. The masses of large bags of pasta are normally distributed with mean 2.50 kg and standard deviation 0.12 kg. Find the probability that the mass of…
Answer this question and get it marked →May–June 2025, Paper 55
The heights of trees in a certain forest are classified as tall, medium or small. The heights can be modelled by a normal distribution with mean 20 m and standard deviation 5 m.…
Answer this question and get it marked →In a certain large school, on average, two pupils in five have music lessons. A random sample of 80 pupils from this school is chosen. Use an approximation to find the probability…
Answer this question and get it marked →May–June 2025, Paper 62
One of a group of three students is to be chosen at random. Explain how a single throw of a fair six-sided dice could be used to make the choice.
Answer this question and get it marked →The amount of time, in minutes, spent by a customer on one visit to a certain shop is modelled by the random variable X ~ N(mu, sigma^2). In the past, the values of mu and sigma…
Answer this question and get it marked →May–June 2024, Paper 51
The lengths of the tails of adult raccoons of a certain species are normally distributed with mean 28 cm and standard deviation 3.3 cm. Find the probability that a randomly chosen…
Answer this question and get it marked →May–June 2024, Paper 52
The weights of oranges can be modelled by a normal distribution with mean 131 grams and standard deviation 54 grams. Oranges are classified as small, medium or large. A large…
Answer this question and get it marked →May–June 2024, Paper 53
In a certain country, the heights of the adult population are normally distributed with mean 1.64 m and standard deviation 0.25 m. Find the probability that an adult chosen at…
Answer this question and get it marked →May–June 2024, Paper 61
The random variable X has the distribution N(31.2, 10.4^2). Two independent random values of X, denoted by X1 and X2, are chosen. Find P(X1 3X2).
Answer this question and get it marked →May–June 2024, Paper 62
The masses of cereal boxes filled by a certain machine have mean 510 grams. An adjustment is made to the machine and an inspector wishes to test whether the mean mass of cereal…
Answer this question and get it marked →May–June 2024, Paper 63
The masses in kilograms of large and small bags of cement have the independent distributions N(50, 2.4) and N(26, 1.8) respectively. Find the probability that the total mass of 5…
Answer this question and get it marked →October–November 2024, Paper 51
The weights of the green apples sold by a shop are normally distributed with mean 90 grams and standard deviation 8 grams. Find the probability that a randomly chosen green apple…
Answer this question and get it marked →The heights of the female students at Breven college are normally distributed: - 90% of the female students have heights less than 182.7 cm. - 40% of the female students have…
Answer this question and get it marked →October–November 2024, Paper 52
The heights, in metres, of white pine trees are normally distributed with mean 19.8 and standard deviation 2.4. In a certain forest there are 450 white pine trees. How many of…
Answer this question and get it marked →October–November 2024, Paper 53
In Molimba, the heights, in cm, of adult males are normally distributed with mean 176 cm and standard deviation 4.8 cm. Find the probability that a randomly chosen adult male in…
Answer this question and get it marked →October–November 2024, Paper 61
The masses, in kilograms, of small and large bags of wheat have the independent distributions N(16.0, 0.4) and N(51.0, 0.9) respectively. Find the probability that the total mass…
Answer this question and get it marked →October–November 2024, Paper 63
The masses, in kilograms, of small and large bags of wheat have the independent distributions N(16.0, 0.4) and N(51.0, 0.9) respectively. Find the probability that the total mass…
Answer this question and get it marked →May–June 2023, Paper 51
A mathematical puzzle is given to a large number of students. The times taken to complete the puzzle are normally distributed with mean 14.6 minutes and standard deviation 5.2…
Answer this question and get it marked →May–June 2023, Paper 52
The lengths of Western bluebirds are normally distributed with mean 16.5 cm and standard deviation 0.6 cm. A random sample of 150 of these birds is selected. How many of these 150…
Answer this question and get it marked →May–June 2023, Paper 53
Anil is a candidate in an election. He received 40% of the votes. A random sample of 120 voters is chosen. Use an approximation to find the probability that, of the 120 voters,…
Answer this question and get it marked →The mass of grapes sold per day by a large shop can be modelled by a normal distribution with mean 28 kg. On 10% of days less than 16 kg of grapes are sold. Find the standard…
Answer this question and get it marked →May–June 2023, Paper 61
Large packets of rice are packed in cartons, each containing 20 randomly chosen packets. The masses of these packets are normally distributed with mean 1010 g and standard…
Answer this question and get it marked →May–June 2023, Paper 63
The mass, in tonnes, of steel produced per day at a factory is normally distributed with mean 65.2 and standard deviation 3.6. It can be assumed that the mass of steel produced…
Answer this question and get it marked →October–November 2023, Paper 51
A farmer sells eggs. The weights, in grams, of the eggs can be modelled by a normal distribution with mean 80.5 and standard deviation 6.6. Eggs are classified as small, medium or…
Answer this question and get it marked →October–November 2023, Paper 52
A factory produces a certain type of electrical component. It is known that 15% of the components produced are faulty. A random sample of 200 components is chosen. Use an…
Answer this question and get it marked →The heights of the members of a club are normally distributed with mean 166 cm and standard deviation 10 cm. Find the probability that a randomly chosen member of the club has…
Answer this question and get it marked →October–November 2023, Paper 53
The weights of large bags of pasta produced by a company are normally distributed with mean 1.5 kg and standard deviation 0.05 kg. Find the probability that a randomly chosen…
Answer this question and get it marked →October–November 2023, Paper 63
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 →Other AS & A Level Mathematics topics
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- Permutations and combinations (27)
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