The hourly count of particulate matter particles P P\,P detected by an atmospheric monitoring sensor follows a Poisson distribution with a mean of 8.4.
A random sample of 50 hours is recorded, and the mean number of particles per hour, Pˉ\bar{P}Pˉ, is calculated.
Specify the approximate distribution for the mean number of particles detected per hour for a random sample of 50 hours.
The hourly count of specific deep-space radio pulses detected by a telescope follows a Poisson distribution with mean μ\muμ.
A random sample of 80 hours of observation is taken and the sample mean count, Sˉ\bar{S}Sˉ, is determined. The width of the 95% confidence interval for μ \mu\,μ is calculated to be 1.2.
Find an estimate for the value of μ\muμ.
A researcher conducts two further independent observation runs of 80 hours each and calculates a 95% confidence interval for μ \mu\,μ for each run.
Determine the probability that the true mean μ \mu\,μ is contained within exactly one of these two new confidence intervals.
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.