The number of microwaves sold by an electronics shop each week can be modelled by a Poisson distribution with mean 5.
A random sample of 45 weeks is taken and the mean number of microwaves sold per week, Mˉ\bar{M}Mˉ, is calculated.
Write down the approximate distribution for the mean number of microwaves sold per week from a random sample of 45 weeks.
The number of coffee machines sold by the shop each week can be modelled by a Poisson distribution with mean μ\muμ.
A random sample of 60 weeks is taken and the mean number of coffee machines sold per week, Cˉ\bar{C}Cˉ, is found. The width of the 95% confidence interval for μ\muμ is 1.4.
Find an estimate for μ\muμ.
A second, independent random sample of 60 weeks is taken and a second 95% confidence interval for μ\muμ is found.
Find the probability that exactly one of these two confidence intervals contains μ\muμ.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.