algebra 2 word problem

Question

Scores on a standard IQ test are approximately Normally distributed with k = 100 and o= 10. What IQ score corresponds to a standardized score of 2.10?

A-9.79

B79

C97.9

D121

Answer 1

Hello, this problem is related to a statistics concept known as the Z-Score (referred to here as the standardized score). We are allowed to use the Z-score here because the distribution is normally distributed.

The formula for Z-Score is:

(x - x_bar) / σ = Z

x is the data point (this is what we are looking for here)

x_bar is the mean of the data (100)

σ is the population standard deviation (10)

Z is the standardized score (2.1)

Here we just need to plug everything into the formula and solve for x as follows:

(x - 100) / 10 = 2.1 (Multiply both sides by 10)

x - 100 = 21 (Add 100 to both sides)

x = 121

So here, an IQ score of 121 will give us a z-score of 2.1 based on the data given. What this means is that the score of 121 is 2.1 standard deviations away from the population mean which can be useful knowledge when trying to perform analysis on how likely it is for someone to have a score like that, etc.

If you need anymore help, please message me!