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 110 and a standard deviation of 15, what is the minimum score a person must have to qualify for the society

The minimum score a person must have to qualify for the society is 140.81.

Step-by-step explanation:

We are given that 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.

Also, test scores are normally distributed with a mean of 110 and a standard deviation of 15.

Let X = test scores

SO, X ~ N()

The z-score probability distribution is given by ;

                  Z = ~ N(0,1)

where, = mean score = 110

            = standard deviation = 15

Now, the minimum score a person must have to qualify for the society so that his score is in the top 2% is given by ;

              P(X ) = 0.02   {where is minimum score required by person}

             P( ) = 0.02

             P(Z ) = 0.02

Now, in z table we will find out that critical value of X for which the area is in top 2%, which comes out to be 2.0537

This means;        

                              = 110 + 30.806 = 140.81

Therefore, the minimum score a person must have to qualify for the society is 140.81.

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