Question

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 (over 100
trials), 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 z-score for this observation of 1,066.
b) Explain why we can describe this problem by using a normal probability distribution!
c) What is the probability that a sample of gold would show a melting point as different from its
average as 1,066 degrees centigrade?
d) Is it likely that this unknown metal is gold?

Answer 1

a) Calculate the z-score for this observation of 1,066.

b) Explain why we can describe this problem by using a normal probability distribution!

We have used a sufficiently large number for sample size, 100. This allows Central Limit Theorem to be applied, which tells us sufficiently large sample means follow the normal distribution.

c) What is the probability that a sample of gold would show a melting point as different from its
average as 1,066 degrees centigrade?

d) Is it likely that this unknown metal is gold?

There is very less chance that this is gold, less than 2.5% which is lower than the significance level of 5%. We can safely reject it as gold.