1) Suppose the average number of students who log on to a university's computer system is 4.45 in each 5-minute interval.

a. What is the probability that six students will log on in the next minute?

b. What is the probability that fewer than six students will log on during the next two minutes?

2) From the Household Expenditure Statistics: Year Ended 30 June 2016, the average weekly household expenditure in New Zealand was $1,300. Assuming that weekly household expenditure is approximately normal with a standard deviation of $350.

a. Find the probability that a household's weekly expenditure is

i. less than $500

ii. more than $1,750

b. What proportion of household expenditures are between $1,250 and $1,500?

c. 99% of households have weekly expenditures of less than which amount?

d. 95% of households have weekly expenditures of more than which amount?

Please answer both 2 question with clear explanation and calculation step by step.

Thank you