An examination is frequently regarded as being designed good if the test scores

Question

An examination is frequently regarded as being designed good if the test scores of those taking the examination is bell-shaped or normally distributed. If the test scores follows a normal distribution with mean equal to and variance equal to 2, the instructor often assigns the letter grade A to those whose test score is greater than + , B to those whose score is between and + , C to those whose score is between - and , D to those whose score is between 20 and -, and F to those getting a score below -2. (This strategy is sometimes referred to as grading "on the curve."). Approximately what percentage of class will receive an A grade on the examination? O 15% o 16% O 17% o 18%

Explanation / Answer

Define random variable X as score of the student ~ N(, 2)

Therefore % of A grade students = 100 * P[X > +] = 100 * P[Z>1] = 15.86553 ~ 16

So, Correct answer is 16%

                                     

Therefore % of C grade students = 100 * P[- < X < ] = 100 * P[-1< Z < 0] = 34.1345 ~ 34

So, Correct answer is 34%

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