A hotel has 160 rooms of which 20 are classified as De-luxe, 40 Premier and 100 as Standard. The manager wants to obtain information about room usage in the hotel by taking a \(10 \%\) sample of the rooms.
Suggest a suitable sampling method.
Explain in detail how the manager should obtain the sample.
A random sample of 100 classical CDs produced by a record company had a mean playing time of 70.6 minutes and a standard deviation of 9.1 minutes. An independent random sample of 120 CDs produced by a different company had a mean playing time of 67.2 minutes with a standard deviation of 8.4 minutes.
Using a \(1 \%\) level of significance, test whether or not there is a difference in the mean playing times of the CDs produced by these two companies. State your hypotheses clearly.
State an assumption you made in carrying out the test in part (a).
The weights of a group of males are normally distributed with mean 80 kg and standard deviation 2.6 kg . A random sample of 10 of these males is selected.
Write down the distribution of \(\bar { M }\), the mean weight, in kg , of this sample.
Find \(\mathrm { P } ( \bar { M } < 78.5 )\).
The weights of a group of females are normally distributed with mean 59 kg and standard deviation 1.9 kg . A random sample of 6 of the males and 4 of the females enters a lift that can carry a maximum load of 730 kg .
Find the probability that the maximum load will be exceeded when these 10 people enter the lift.