QUESTION 2 [20 MARKS] a. The ages of people at a party are normally distributed with mean 30 years and variance 36 years. If a person at this party is randomly chosen, calculate the probability (to four decimal places) that the person is:

i. Less than 35 years of age. (3 marks)

ii. More than 20 years of age. (3 marks)

b. From experience, 40 out of every 100 students sitting for STA116 pass the examination. A sample of 10 students was chosen. What is the probability that:

i. Exactly 3 students will pass? (3 marks)

ii. At least 7 students will fail? (4 marks)

c. Machine breakdowns occur at a rate of 6 per week. Calculate the probability that:

i. No breakdowns occur in a given week. (3 marks)

ii. Less than 3 breakdowns occur in a given 3 weeks. (4 marks)