For large classes, test scores are usually approximately normally distributed. S

Question

For large classes, test scores are usually approximately normally distributed. Suppose 500 students have taken a Statistics test. The distribution of scores is approximately Normal with mean 79.68 and standard deviation 17.91 (these happen to be the values from your first midterm exam).

(a) What proportion of students received an “A” ( 90 points) on the test?

(b) If a professor “curves” a class, that means that the professor uses the exam score distribution itself to assign grades. Where would the professor have set the A/B cutoff if she would have wanted to assign A’s to the top 15% of the class?

Explanation / Answer

Here it is given mean=79.68 and sd=17.91

a. We need to find P(x>=90), as it is given that distribution is normal we will convert x to z.

P(x-mean/sd>=90-79.68/17.91)=P(z>=0.576)=0.5-P(0<=z<=0.576)=0.5-0.2177=0.2823

b. Here he want to find x such that P(X>x)=0.15

Using z table we get P(Z>z)=0.15 for z=1.036=x-79.68/17.91

So x=1.036*17.91+79.68=98.23476

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