Answer:
95%
Explanation:
The 68-95-99.7 rule to find the percentage of people is also know as the empirical rule.
The empirical rule formula states that:
68% of data falls within 1standard deviations from the mean - between μ – σ and μ + σ .
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .
From question:
Mean (μ) = 505
Standard deviation (σ) = 146
Hence, we are to find the number of standard deviation which is represented as x
The score is between 213 and 797
μ - xσ
= 505 - 146x = 0
= 505 - 146x = 213
146x = 505 - 213
146x = 292
x = 292/146
x = 2
μ + xσ
505 +146x = 797
146x = 797 - 505
146x = 292
x = 292/146
x = 2
Hence, the percentage falls within 2 standard deviation from the mean.
Thus, from the formula above:
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
Therefore, the percentage of people taking the test who score between 213 and 797 is 95%