Learn Extracted exam questions A-Level Mathematics 9709 Mathematics June 2025 Question Paper 51
9709 Mathematics June 2025 Question Paper 51
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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 this rice is less than 1.48 kg is 0.22. Find the value of $\mu$.
Find the number of different arrangements of the 8 letters in the word KANGAROO in which the two As are together and the two Os are not together.
A fair 8-sided dice has faces labelled K, A, N, G, A, R, O, O. The dice is rolled repeatedly. Find the probability that fewer than 6 rolls of this dice are required to obtain an A.
Find the probability that the second A is obtained on the 6th roll of the dice.
Last Sunday, teams of runners took part in a charity event. The time taken, in seconds, to run 50 m was recorded, correct to 1 decimal place, for each runner. The times recorded for 11 runners from each of the Gulls and the Herons are shown in the table. Gulls: 7.9, 8.2, 8.3, 8.6, 8.6, 8.8, 9.2, 9.7, 9.8, 10.0, 10.4. Herons: 9.5, 9.9, 8.5, 8.1, 9.2, 10.8, 8.3, 9.7, 9.3, 9.9, 8.7.
Draw a back-to-back stem-and-leaf diagram to represent this information, with Gulls on the left-hand side.
Find the median and the interquartile range of the times of the runners from the Gulls.
Two other teams, the Eagles and the Swifts, also took part. The recorded times in seconds for 20 runners from the Eagles and 30 runners from the Swifts are denoted by $x$ and $y$ respectively. It is given that $\sum x = 175.0$ and that the mean of $y$ is 8.4. Find the mean of the times taken by all 50 runners.
It is given that $\sum x^2 = 1823.0$. It is also known that the standard deviation of the times taken by all 50 runners is 1.38 seconds. Find the value of $\sum y^2$, correct to 1 decimal place.
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, 600 competitors took part. The times taken to complete the puzzle were normally distributed with mean 32.4 minutes and standard deviation 2.5 minutes.
How many competitors would you expect to have times within 1.2 minutes of the mean time?
In this Saturday's event, 60% of the competitors had times less than 36.0 minutes. 9 competitors who took part are selected at random. Find the probability that at least 2 and fewer than 8 of these competitors had times less than 36.0 minutes.
80 competitors who took part in this Saturday's event are selected at random. Use a suitable approximation to find the probability that more than 50 of these competitors had times less than 36.0 minutes.
In a group of 20 musicians, there are 9 guitarists, 6 pianists and 5 drummers. 6 musicians are selected from these 20 to perform at a concert.
Find the number of different ways in which the 6 musicians can be selected if there must be at least 3 guitarists, at most 2 pianists and exactly 1 drummer.
Three bands will be selected from the original group of 20 musicians. Each band will consist of 3 guitarists, 1 pianist and 1 drummer. No musician can be in more than one band. The first band selected will play in France, the second in Italy and the third in Spain. Find the number of different ways in which these three bands can be selected.
A bag contains 10 marbles, of which 4 are red and 6 are blue. Four marbles are selected from the bag at random, without replacement. The random variable $X$ denotes the number of blue marbles selected.
Show that $\mathrm{P}(X = 2) = \tfrac37$.
Draw up the probability distribution table for $X$.
Find the probability that at least 2 of the marbles chosen are blue, given that at least 1 red marble and at least 1 blue marble are chosen.