Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).
the grades received by 200 students follow a normal distribution. the mean of the grades is 70%, and the standard deviation is 7%.
the number of students who received a grade greater than 70% is about
, and the number of students who got a grade higher than 84% is about

Explanation:

Step1: Find z-score for 70%

Since 70% is the mean ($\mu=70\%$), $z=\frac{70-\mu}{\sigma}=\frac{70-70}{7}=0$

Step2: Find % above mean

In normal distribution, 50% of data is above the mean.

Step3: Calculate students above 70%

$200 \times 0.5 = 100$

Step4: Find z-score for 84%

$z=\frac{84-\mu}{\sigma}=\frac{84-70}{7}=2$

Step5: Find % above z=2

In normal distribution, ~2.28% of data is above $z=2$.

Step6: Calculate students above 84%

$200 \times 0.0228 \approx 5$

Answer:

100, 5