Question

A person must score in the upper 2% of the population on an admissions test to qualify for membership in society catering to highly intelligent individuals. If test scores are normally distributed with a mean of 140 and a standard deviation of 15, what is the minimum score a person must have to qualify for the society? (Round your answer to the nearest integer.)

Answer 1

Consider X : score

We have given the "Normal distribution "

We have given the Upper area as the 2%

We convert that area into Decimal

Upper Area = 0.02

We calculate the Remaining area i.e left tail area

Left tail area = 1 - Upper Area = 1 - 0.02 = 0.9800

Now we find the Z score for the area 0.9800

We use the Z table for it

Now we use the Z table to find the Z score for the area 0.9800

Look the uploaded table

We look for the area which is very close to 0.9800 and we get the area which is very close is 0.9798

So we get the Z score as 2.05

We have mentioned the rounding as round to " Nearest Integer "

So we get the answer as

x = 171

Final Answer :-

171 is the Minimum score of person   which must have to qualify the society