Question
1) Consider a class with a normal distribution of grades of 5.5. The standard deviation is 0.5. Calculate the percentage of students who obtained a grade: A) between 5 and 6; B) above 6; C) below 5.
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Answer to a math question 1) Consider a class with a normal distribution of grades of 5.5. The standard deviation is 0.5. Calculate the percentage of students who obtained a grade: A) between 5 and 6; B) above 6; C) below 5.
Hank
4.897 Answers
A) between 5 and 6
1. Convert grades to z-scores: Z = \frac{X - \mu}{\sigma}
Z_1 = \frac{5 - 5.5}{0.5} = -1
Z_2 = \frac{6 - 5.5}{0.5} = 1
2. Calculate cumulative probabilities:
P(-1 \leq Z \leq 1) = P(Z \leq 1) - P(Z \leq -1)
0.8413 - 0.1587 = 0.6826
3. Convert to percentage:
68.26\%
B) above 6
1. Convert grade to z-score: Z = \frac{X - \mu}{\sigma}
Z = \frac{6 - 5.5}{0.5} = 1
2. Calculate cumulative probability:
P(Z > 1) = 1 - P(Z \leq 1)
1 - 0.8413 = 0.1587
3. Convert to percentage:
15.87\%
C) below 5
1. Convert grade to z-score: Z = \frac{X - \mu}{\sigma}
Z = \frac{5 - 5.5}{0.5} = -1
2. Use cumulative probability:
P(Z < -1) = 0.1587
3. Convert to percentage:
15.87\%
Answer:
A) 68.26\%
B) 15.87\%
C) 15.87\%
1. Convert grades to z-scores:
2. Calculate cumulative probabilities:
3. Convert to percentage:
B) above 6
1. Convert grade to z-score:
2. Calculate cumulative probability:
3. Convert to percentage:
C) below 5
1. Convert grade to z-score:
2. Use cumulative probability:
3. Convert to percentage:
Answer:
A) 68.26\%
B) 15.87\%
C) 15.87\%
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