Answer to Question #268334 in Statistics and Probability for Haze

Question

The Emotional Quotient (EQ) score on the latest version of Surge EQ Test is transformed so as to follow a normal distribution with a mean of 100 and standard deviation of 15. Find the 95^th percentile of the distribution of Emotional Quotient.

 

Solution:

1: Draw a figure and represent the area.

2: Find the z value.

3: Answer the question

Answer 1

1.

A figure representing the area is as given below

2.The z value can be determined by entering the following command in $R$

> qnorm(0.95)

The output is,

[1] 1.644854

Therefore, the z value is 1.644854

3.

Let $X$ be the 95^th percentile then, we use the formula given below to find its value as follows,

$X=\mu +Z\sigma$

Therefore,

$X=100+(1.644854*15)=100+24.67281=124.67281$

Thus, the 95^th percentile is X=124.67281