Assignment 6/33

Question 1: The wait time for a bus is anytime between 0 and 20 minutes equally randomly. Create a probability density function and related graph. What is the probability that the wait for the bus will be in between 2 and 5 minutes? (3 marks for density function, 3 marks for density graph and 3 marks for problem)

Question 2: The length of stay of patients suffering from a sickness is normally distributed with a mean length of stay of 15 days and a standard deviation of 5 days. Seven thousand people were treated for a sickness in January.

a)If a patient stays 9 days, what is the corresponding z-score. (3 marks)

b)How many patients had a length of stay less than 9 days? (3 marks)

Question 3: The mean lifetime of the engine of a particular car is 250,000 km with a standard deviation of 50,000 km. (3 marks each)

a)What is the probability that an engine will last more than 375,000 km?

b)What is the probability that an engine will last less than 125,000 km?

c)What is the probability that an engine will last in between 375,000 km and 125,000 km?

d)A warranty lasts up to 125,000 km. If the manufacture sells 50,000 cars with this warranty and an engine replacement costs $2,500, what is the expected warranty cost using this model?

Question 4: A poll questioned 500 students about their views on pizza for lunch at school. The results indicated that 75% of respondents felt that pizza was a must for lunch at school and would quit school if there was no pizza at lunch.

a)Determine the 90% confidence interval. (5 marks)

b)What is the margin of error for this response at the 90% confidence level? (1 mark)