Question

The mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points. What is the z score test result of 1300 points?

Answer 1

z score is 1.33 approximately.

Explanation:

Given:

mean score= 1700 points

standard deviation= 75 points

value of interest =1300 points

To Find:

z score=?

Solution:

z-score:

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean, and negative if it lies below the mean.

The formula to solve for z-scores is:

`z=(X-\mu)/(\sigma)`------------------------------------(1)

where,

X is the value of interest,

μ is the mean of the normal distribution,

σ is the standard deviation of the normal distribution.

Substituting the values in the equation (1), we have

`z=(1800-1700)/(75)`

`z=(100)/(75)`

`z=(4)/(3)`

`z \approx 1.33`