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The scores on a psychology exam were normally distributed with a mean of 57 and a standard deviation of 9. A failing grade on the exam was anything 2 or more standard deviations below the mean. What was the cutoff for a failing​ score? Approximately what percentage of the students​ failed?

Respuesta :

shinmin
Given:Sample mean= 57 

Standard Deviation= 9 
score of 59 

we go to our standard formula: 


(score - mean) / sd = z 
(59 - 57) / 9 = z 

2/9 = z 

0.2222 = z
Failing score cutoff would be equal to Mean - 2SD = 67 - 2(9) = 48 is failing score cutoff.
ernikhil

The cutoff for a failing​ score is [tex]39[/tex] with [tex]22.22\%[/tex] of the students​ failed.

Following the general formula, [tex]z=\dfrac{\rm Score-Mean}{\rm Standard\;Deviation}[/tex]

According to the question, the scores on a psychology exam were normally distributed with a mean of 57 and a standard deviation of 9. A failing grade on the exam was anything 2 or more standard deviations below the mean so,

[tex]z=\dfrac{\rm Score-Mean}{\rm Standard\;Deviation}\\z=\dfrac{2}{9}\\z=0.222[/tex]

Also, falling cut-off score is calculated as-

[tex]\rm Falling\;cut-off=Mean-2\times Stand\;Deviation\\\rm Falling\;cut-off=57-2\times 9\\\rm Falling\;cut-off=57-18\\\rm Falling\;cut-off=39[/tex]

Hence, cutoff for a failing​ score is [tex]39[/tex] with [tex]22.22\%[/tex] of the students​ failed.

Learn more about mean and standard deviation here:

https://brainly.com/question/10729938?referrer=searchResults