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the mean score of a mathematics placement exam is 125 with a standard deviation of 12.51. those who score i the bottom 20% are required to take a remedial course. assuming the data are not normally distributed, what is the lowest score you can get and not have to take the remedial math class?

Respuesta :

LammettHash
You're looking for [tex]k[/tex] such that

[tex]\mathbb P(X<k)=0.20[/tex]

Transforming the standard normal distribution, you have

[tex]\mathbb P(X<k)=\mathbb P\left(\dfrac{X-125}{12.51}<\dfrac{k-125}{12.51}\right)=\mathbb P(Z<k^*)[/tex]

where [tex]k^*[/tex] is the cutoff score in terms of this new distribution. The z-score corresponding to a probability of 0.20 is approximately [tex]z=k^*=-0.8416[/tex], which means the cutoff test score is

[tex]k^*=\dfrac{k-125}{12.51}\implies k=125+12.51k^*\approx114.47[/tex]

Rounding to the nearest whole point, a score of about 114 is the bare minimum requirement to not have to take the remedial course.

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