Question
The mean score on a test is 75
with a standard deviation of 4.
What range contains about 95%
of the scores?
Select the correct value in each drop-down.
Click Here for a Hint
(2 points)
between(63,67,71,or 73)and(77,79,83,or 87)
with a standard deviation of 4.
What range contains about 95%
of the scores?
Select the correct value in each drop-down.
Click Here for a Hint
(2 points)
between(63,67,71,or 73)and(77,79,83,or 87)
Answers
GPT-4o mini
To find the range that contains about 95% of the scores, we can use the properties of a normal distribution. The empirical rule states that approximately 95% of the data falls within two standard deviations of the mean.
Given:
- Mean (μ) = 75
- Standard deviation (σ) = 4
We can calculate two standard deviations below and above the mean:
1. Two standard deviations below the mean:
\[ μ - 2σ = 75 - 2(4) = 75 - 8 = 67 \]
2. Two standard deviations above the mean:
\[ μ + 2σ = 75 + 2(4) = 75 + 8 = 83 \]
Thus, the range containing about 95% of the scores is between **67** and **83**.
In the dropdown options:
- The correct choice is between (67) and (83).
Given:
- Mean (μ) = 75
- Standard deviation (σ) = 4
We can calculate two standard deviations below and above the mean:
1. Two standard deviations below the mean:
\[ μ - 2σ = 75 - 2(4) = 75 - 8 = 67 \]
2. Two standard deviations above the mean:
\[ μ + 2σ = 75 + 2(4) = 75 + 8 = 83 \]
Thus, the range containing about 95% of the scores is between **67** and **83**.
In the dropdown options:
- The correct choice is between (67) and (83).