Question

A math teacher’s midterm is worth 200 points. The mean of the test is 143 and the standard deviation is 15.7. If the scores have a bell shaped distribution, what percentage of the scores are between 111.6 and 174.4?

A. About 99.7%
B. About 68%
C. About 62.8%
D. About 95%

Answer 1

The answer is D: about 95%.

Answer 2

Answer with explanation:

Mean,

$\mu=143\\\\X_{1}=111.6\\\\X_{2}=174.4$

Standard Deviation $\sigma=15.7$

Total Population = 200

Formula for Z Score and calculation of two Z scores.

$Z_{1}=\frac{\bar X_{1} - \mu}{\sigma}\\\\Z_{1}=\frac{111.6-143}{15.7}\\\\Z_{1}=\frac{-31.4}{15.7}=-2$

Similarly,

$Z_{2}=\frac{174.4-143}{15.7}\\\\Z_{2}=\frac{31.4}{15.7}=2$

So the two values that is , 111.6 and 174.4 , lies 2 standard deviation on left and 2 standard deviation on the right of mean.

→With the Help of Z table, the conclusion can be drawn that, 95 % of Data will lie within two standard deviation that is above and Below the Mean.

Option D: About 95%