5 The mass, in kilograms, of rocks in a certain area has mean 14.2 and standard deviation 3.1.
- Find the probability that the mean mass of a random sample of 50 of these rocks is less than 14.0 kg .
- Explain whether it was necessary to assume that the population of the masses of these rocks is normally distributed.
- A geologist suspects that rocks in another area have a mean mass which is less than 14.2 kg . A random sample of 100 rocks in this area has sample mean 13.5 kg . Assuming that the standard deviation for rocks in this area is also 3.1 kg , test at the \(2 \%\) significance level whether the geologist is correct.