Answer to Question #180638 in Statistics and Probability for Joshua Cornfield

Question

The results of a history exam reveals a normal distribution of marks with an average of 67% and a standard deviation of 5%. READ THE QUESTIONS CAREFULLY.

The TOP 94.52% of students scored at least what grade on the test?

Answer for part 1

%

The bottom 0.02% of students scored equal to or lower than what mark?

Answer for part 2

%

Answer 1

$\mu=67,\sigma=5$

n=100

TOP 94.52% of students scored at least marks= $\mu-z_{0.0025}\dfrac{\sigma}{\sqrt{n}}$

$=67-1.96\dfrac{5}{\sqrt{100}}=67-0.98=66.02$ %

The bottom 0.02% of students scored equal to or lower than what mark

$=\mu+z_{0.0001}\dfrac{\sigma}{\sqrt{n}}$

$=67+3.042\times \dfrac{5}{\sqrt{100}}=67+1.521=68.521$ %