The melting point of gold is known to be approximately 1,060 degrees centigrade. This is, of course, an average figure, for unavoidable ‘experimental error’ causes more or less variation from this figure whenever the test is actually performed. The best measure of these variations is the standard deviation,. Suppose this has been calculated from a large series of tests, and found to be 3 degrees centigrade. Due to the recent increase in the price of gold, special attention may be necessary to confirm that a product is actually gold. Suppose an investigator is analyzing an unknown metal, and a test shows its melting point to be 1,066 degrees centigrade.
a)Calculate the zscore for this observation of 1,066.
b) What is the probability that a sample of gold would show a melting point as different from its average as 1,066 degrees centigrade?
c) Is it likely that this unknown metal is gold?