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The scores on a psychology exam were normally distributed with a mean of 57
and a standard deviation of 4. 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 :

Answer:

Cutoff for a failing score is 49 and 2.28% students failed.

Step-by-step explanation:

We have been given that scores on a psychology exam were normally distributed with a mean of 57  and a standard deviation of 4.

2 standard deviation below mean would be,

[tex]57-2(4) =57-8= 49[/tex]

Therefore,Cutoff far a failing score is 49.

Now let us find out the z-score for our given values,

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{49-57}{4}=\frac{-8}{4} =-2[/tex]

Now let us look up the probability from normal distribution table.

[tex]P(z<-2) =0.02275[/tex]

Therefore, percentage of students failed is 2.28%.



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