Understaing the significance test

statistics

#1

I saw one question regarding Z test (Que.3) in this article

A test is administered annually. The test has a mean score of 150 and a standard deviation of 20. If Ravi’s z-score is 1.50, what was his score on the test?

A) 180
B) 130
C) 30
D) 150
E) None of the above

I am not able to understand the explanation for the answer. Can someone please explain how the answer is A. I have the idea about the z test and its formulation.

Thanks


#2

Hi @neha30,

The explanation includes simply imputing the values in the formula (Z as 1.5, σ as 20 and μ as 150) . Are you facing an issue in understanding the formula - X= μ+Zσ ?


#3

Hi @neha30,

z value is a normalized scale to check how far the value is from mean in terms of standard deviation.

if z of a value is equal to 1, then we say that value is 1 times standard deviation farther from mean.
in your case mean is 150. standard deviation is 20 and z is 1.5. It means that it says, value is 1.5 times standard deviation(20) father from mean(150).

1.5 times 20 = 30. so value is 30 farther than 150(mean). now z is positive it means that value is on right side of mean so we have to add 30 to 150. so the answer is 180.

Hope I made it easier for you to understand.


#4

Yeah, now it’s clear to me. Thanks for the explanation @VikasJangra.