Question

Which is more likely, observing a score less than 100, but greater than 80 sampled at random from a normal distribution with a mean of 72 and a standard deviation of σ = 20, or a score less than 6 sampled at random from a normal distribution with a mean of 5 and an unknown standard deviation of σ, and why?

Answer 1

Solution:

It is more likely to see a score less than 6 sampled at random from a normal distribution with a mean of 5 and an unknown standard deviation because the area less than 6 in the second case will be more than the area between 80 and 100 in the first case.

Now if see the area less than 6 in the second case:

This area will be at least 50% because if we consider the least case of standard deviation = 0, the area less than z=0 is 0.50.

Therefore, it is more likely to see the score less than 6 in the second case.