4. The number of A-grades, \(X\), achieved in total by students at Lowkey School in their Mathematical examinations each year can be modelled by a Poisson distribution with a mean of 3 .
a. Determine the probability that, during a 5 -year period, students at Lowkey School achieve a total of more than 18 A-grades in their Mathematics examinations.
b. The number of A-grades, \(Y\), achieved in total by students at Lowkey School in their English examinations each year can be modelled by a Poisson distribution with mean of 7 .
i. Determine the probability that, during a year, students at Lowkey School achieve a total of fewer than 15 A-grades in their Mathematics and English examinations.
ii. What assumption did you make in answering part (b)(i)?
[0pt] [Total 7 marks]