Question 1

Consider the case offamilies in a small town. A researcher wants to describe the average number of children in each family. If the true population mean,and variance , is .

a) Explain what may have happened for the researcher to record a sampling mean ,

which is different from the population mean?

State whether or not this difference could be attributed entirely to some mistakes in the collection of the sample. [7MARKS]

b) Comment on the population variance and propose how best this estimator could be better enhanced. [6MARKS]

Of the bolts manufactured for a certain application,meet the length specification and can be used immediately,are too long and can be used after being cut and are too short and must be scrapped.

c) Find the probability that a randomly selected bolt can be used

. [6MARKS] d) Find the probability that fewer thanout of a sample ofbolts can be used

[6MARKS]