Suppose. Population of test-scores is normally distributed with mean 65 and standard deviation 13 x~n (65,13) if you select a test at randome what is the probability that the score is below 60 or that it is between 65 and 70 please show work!

Answer 1

I am reading your question as 65 with a standard deviation of 13. This is a population, we will use z-scores and the normal table.

Below 60

(60 -65)/13 = z-score
You can then use the z-table(normal table) to find the area under the lower tail and this will give you the probability of a score under 60

Between 65 and 70
You have to find both z-scores:

(65-65)/13 = 0 that will be right in the middle of the normal table.

(70-65)/13 = z.

using the table, you have to find the area between 65 and 70.

Since there are different versions of z-tables (depending on the textbook), I can't give you further directions regarding reading your z-table.