A researcher wishes to take a sample of size 9 , without replacement, from a list of 72 people involved in the trial of a new computer keyboard. She numbers the people from 01 to 72 and uses the table of random numbers given in the formula book. She starts with the left-hand side of the sixth row of the table and works across the row. The first two numbers she writes down are 56 and 32 .
Find the other six numbers in the sample.
Give one advantage and one disadvantage of using random numbers when taking a sample.
(2 marks)
The length of time that registered customers spend on each visit to a supermarket's website is normally distributed with a mean of 28.5 minutes and a standard deviation of 7.2 minutes.
Eight visitors to the site are selected at random and the length of time, \(T\) minutes, that each stays is recorded.
Write down the distribution of \(\bar { T }\), the mean time spent at the site by these eight visitors.
(2 marks)
Find \(\mathrm { P } ( 25 < \bar { T } < 30 )\).
(4 marks)