Part A

Using your own words explain intuitively what a sampling distribution is, and what information it provides us about a random variable.Explain why the central limit theorem is so important.

Part B

Once again consider the lifetimes of a certain type of calculator battery that are normally distributed with a mean of 400 days and a standard deviation of 50 days.Suppose now that a sample of 100 batteries is taken from the production process.

Determine the following:

1.The probability that the sample mean lifetime is less than 397 days. (2 marks)

2.The probability that the sample mean lifetime is between 397 and 403 days. (3 marks)

Part C

If it is believed that the true proportion of voters who support a major party is 0.55, what is the probability that a sample of size 400 yields a sample proportion of supporters between 0.54 and 0.56?(4 marks)