Question

Student grades in a sufficiently large class tend to follow a normal distribution. Suppose the final exam of a class follows a normal distribution with a mean of 75 and a standard deviation of 7.5. Select a score of 95 and specify its z-score based on this distribution.

When calculating the z-score, include the steps leading to the workings. That way, any mistakes can be quickly seen and corrected. Use the chosen raw score (95) and the calculated z-score to provide a letter grade for the student. Based on these, convey a message to the audience and if possible, indicate your conclusion(s) and/or recommendation(s), if any. For example, would you recommend the student for scholarship? Is the student's performance not as good and you recommend some form of help, e.g., tutoring?

Answer 1

here from the above problem

the given is a normal distribution so,

mean = 75 and standard deviation = 7.5

we know that,

Z = (X - mean) / standard deviation = (95 - 75) / 7.5 = 2.6667

from the above Z - value we have to calculate the P - value,

here we have to consider a two tail method, So

P(Z = 2.6667) = 0.0077

hence p - value is less than 0.01.  

so the the student's performance not as good and we recommend some form of help (tutoring)

please revert if any doubts