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.
