normal distribution

Question

The scores of a test given to students are normally distributed with a mean of 21.
80 % of the students have scores less than 23.7.
(a) Find the standard deviation of the scores.

Answer 1

(x - mean) / sd = z

 

x = 23.7

mean = 21

 

For the p-value to be 80%, we can look on the z-score table to see how many SDs away from the mean 80% of the data would be. This would be z = .84 SDs.

 

So now we can just plug in and solve.

 

(23.7 - 21)/sd = .84

2.7 = .84sd

3.214 = sd