3. Explain what you understand by
- a statistic,
- a sampling distribution.
A factory stores screws in packets. A small packet contains 100 screws and a large packet contains 200 screws. The factory keeps small and large packets in the ratio 4:3 respectively.
- Find the mean and the variance of the number of screws in the packets stored at the factory.
A random sample of 3 packets is taken from the factory and \(Y _ { 1 } , Y _ { 2 }\) and \(Y _ { 3 }\) denote the number of screws in each of these packets.
- List all the possible samples.
- Find the sampling distribution of \(\bar { Y }\)