Answer:
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.
<em>Let X = test scores</em>
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
<em>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 </em><u><em>2.0537</em></u><em> </em>
This means;
= 110 + 30.806 = <u>140.81</u>
Therefore, the minimum score a person must have to qualify for the society is 140.81.