AS & A Level Mathematics (9709) — 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.

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,…

The random variable X has the distribution Po(15). Write down an expression in terms of e for P(X = 12).

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…

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…

Use suitable approximating distributions to answer the following. The random variable W has the distribution B(700, 0.005). Find P(W = 4).

The random variable X has probability density function given by f(x) = kx^2 / a^2 for 0 <= x <= a, f(x) = 0 otherwise, where k and a are positive constants. Show that k = 3/a.

Birgitte has a six-sided dice. She suspects that the dice is biased so that the probability, p, that it will show a six on one throw is less than 1/6. She throws the dice 30 times…