The number of heaters, \(H\), bought during one day from Warmup supermarket can be modelled by a Poisson distribution with mean 0.7
Calculate \(\mathrm { P } ( H \geqslant 2 )\)
The number of heaters, \(G\), bought during one day from Pumraw supermarket can be modelled by a Poisson distribution with mean 3, where \(G\) and \(H\) are independent.
Show that the probability that a total of fewer than 4 heaters are bought from these two supermarkets in a day is 0.494 to 3 decimal places.
Calculate the probability that a total of fewer than 4 heaters are bought from these two supermarkets on at least 5 out of 6 randomly chosen days.
December was particularly cold. Two days in December were selected at random and the total number of heaters bought from these two supermarkets was found to be 14
Test whether or not the mean of the total number of heaters bought from these two supermarkets had increased. Use a \(5 \%\) level of significance and state your hypotheses clearly.