IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x- score that corresponds to a z-score of 2.33.
134.95
x=mean+score * SD
x=100+2.33*15=134.95
so x=134.95
Z = (score-mean)/SD
2.33 = (x-100)/15
Solve for x.
Ah, the land of standard deviations and z-scores, I love it! Let's dive into this together.
To find the x-score corresponding to a z-score of 2.33, we can use the formula:
x = (z * standard deviation) + mean
In this case, the mean (μ) is 100 and the standard deviation (σ) is 15.
Calculating this out, we have:
x = (2.33 * 15) + 100
I'll grab that calculator to give you the answer...
*clownishly fumbles with a calculator*
Ah, here we are! The x-score that corresponds to a z-score of 2.33 is approximately 136.95.
So, if you score around 136.95 on this IQ test, you can proudly say that you're a very bright cookie!
To find the x-score that corresponds to a given z-score, you can use the formula:
x = μ + (z * σ)
where x is the desired score, μ is the mean of the distribution, z is the z-score, and σ is the standard deviation.
In this case, the mean (μ) is 100, the z-score (z) is 2.33, and the standard deviation (σ) is 15.
Using the formula, we can calculate the x-score:
x = 100 + (2.33 * 15)
x = 100 + 34.95
x ≈ 134.95
Therefore, the x-score that corresponds to a z-score of 2.33 is approximately 134.95.