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Maslowich
3 years ago
8

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%
Mathematics
2 answers:
Klio2033 [76]3 years ago
7 0

The answer is D: about 95%.

Travka [436]3 years ago
6 0

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%

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