Part (a)

State three (3) characteristics of the Normal Distribution. [3marks]

Part (b)

The times taken by employees of a bauxite company to travel to work follow a Normal Distribution with mean 80 minutes and standard deviation 24 minutes.

Find the probability that a randomly selected employee travelling to work takes:

1. more than 116 minutes.
2. between 80 and 130 minutes [3+4marks]

Part (c)

A researcher is interested in determining the proportion of customers at a local commercial bank, who due to poor customer service, have decided or is planning to leave the bank. In a random sample of 60 customers who complained about poor customers, 15 had decided or is planning to leave the bank.

Develop the 95% confidence interval for the proportion of all customers who experienced poor customer service, that have decided or is planning to leave the bank.

[7marks]

Part (d)

The Real Juice Company is concerned that the 560 ml bottles are being overfilled. The quality control department took a random sample of 70 bottles and found that the mean volume was 564 ml, with standard deviation 9 ml. At the 1% level of significance, can it be concluded that the bottles are being overfilled? [8 marks