1. Historical records reveal that the scores on an entry test to an exclusive college follows a normal distribution with a mean of 65 and a standard deviation of 10.
2. Determinethe probability that a randomly selected student who sits the test will score at least 77.
3. If the college wants only 8% of applicants to pass the test,determinethe test score should they set as the pass mark.

1. When a milling machine is working properly it produces hose fittings with a diameter which is normally distributed with a mean of 19mm and a standard deviation of 0.02 mm.
2. A randomly sampled hose fitting is measured and found to have a diameter of 18.98 mm.Determinethe probability of getting a diameter of no more than 18.98mm if the machine is working properly.Explainwhether this suggests the machine is not working properly.

1. A random sample of 10 hose fittings is then taken and found to have an average 18.98 mm.Determinethe standard error of the sample mean.

1. Determinethe probability of getting an average diameter of no more than 18.98mm, if the machine is working properly.Explainwhether this should cause you to change your previous conclusion as to whether the machine is working properly.

1. Rather than taking a random sample as requested, the machine operator simply sampled the first 10 hose fittings produced.What type of sampling approachis this andexplainwhether it affects the validity of our conclusion to part (iii)