Given that the results of a particular mathematics exam are typically normally d

Question

Given that the results of a particular mathematics exam are typically normally distributed with a mean of 75% between all sections, answer the following questions (a) Suppose a student scores 90% on the exam. Would you consider this students score to be significantly high? Why or why not? (b Suppose a certain class of 30 students had an average of 90% on the exam. Would you consider this class's average to be significant y high? Why or why not? ke sure your answers use statistical reasoning and that you clearly label your answers to (a) and (b)

Explanation / Answer

(A)

mean = 0.75

std. dev. = sqrt(0.75*0.25/1) = 0.433

P(pcap > 0.9) = P(z > (0.9 - 0.75)/0.433) = P(z > 0.3464) = 0.3645

As p-value is greater than 0.05, we can say that 90% score is not significantly high.

(B)

mean = 0.75

std. dev. = sqrt(0.75*0.25/30) = 0.0791

P(pcap > 0.9) = P(z > (0.9 - 0.75)/0.0791) = P(z > 1.8974) = 0.029

As p-value is less than 0.05, we can conclude that 90% score is significantly high.

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