D

The distribution of reading scale scores in an Elementary School was approximately normal with mean \mu = 257 and standard deviation \sigma = 36.
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Anonymous
0

Educational researchers are conducting an intervention experiment. To participate in the experiment, a student must have a reading scale score in the lower 25% of the scores in their grade level.


What is the maximum reading scale score for students to participate in the intervention experiment?

Sangeetha Pulapaka
0

Lower 25% means to the bottom in the normal distribution curve.

So, we pick a value of z. We do that using a z-score table. Note that the value is at the bottom of the curve, so it will be a negative value, and we have to get the value as close as we can to 0.25.




So, the z-score from the z-table is \approx -0.67

Now we can find the duration that corresponds to a z=−0.67  by plugging in the given values in


z = \frac{x - \mu}{\sigma} to get,

-0.67 = \frac{x - 257}{36}

   \Rightarrow -24.12 = x - 257

\Rightarrow x = 232.88


We could get a more accurate answer by using the inverse normal function on a calculator:

https://www.wolframalpha.com/widgets/gallery/view.jsp?id=540d8e149b5e7de92553fdd7b1093f6d


to get x = 232.718


So, the maximum reading scale score for students to participate in the intervention experiment is approximately 232.