Question 1 [4 marks]

Part a) (2 marks)

Find the following probabilities by checking the z table i) P((Z>-0.8)

ii) P(-0.85

iii) Z0.2

Part b) (2 marks)

A new car has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles. Find the probability of the following events.

i) The car travels more than 70 miles per gallon. ii) The car travels less than 60 miles per gallon.

iii) The car travels between 55 and 70 miles per gallon.

Question 2 [4 marks]

Part a) (2 marks)

We assume that X is normal distributed with the mean value =800 and standard deviation

=100. Suppose the sample size n=16, find the following.

i) P( X >750)

ii) P(750< X <1000)

Part b) (2 marks)

The heights of children two-years-old are normally distributed with a mean of 32 inches and standard deviation of 1.5 inches.

i) Find the probability that a two-year-old child is between 30 and 33 inches tall.

ii) If 9 children are randomly selected, find the probability that their mean heights exceed

30 inches.

Question 3 [6 marks]

Part a) (3 marks)

Given the following information

X =500, =12, n=50

Determine the 95% confidence interval estimate of population mean.

Part b) (3 marks)

A statistics practitioner calculated the mean and standard deviation from a sample of 51. They are X =120 and s=15.

Estimate the population mean with 95% confidence level.

Question 4 [6 marks]

The number of pages printed before replacing the cartridge in a laser printer is normally distributed with a mean of 11,500 pages and a standard deviation of 800 pages. A new cartridge has just been installed.

Part a) (3 marks)

What is the probability that the printer produces more than 12,000 pages before this cartridge must be replaced?

Part b) (3 marks)

What is the probability that the printer produces fewer than 10,000 pages?