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Answer:
The percent of students who scored below 62 is 2.3%.
Step-by-step explanation:
In statistics, the 68–95–99.7 rule, also recognized as the empirical rule, is used to represent that 68.27%, 95.45% and 99.73% of the values of a Normally distributed data lie within one, two and three standard deviations of the mean, respectively.
Then,
- P (-1 < Z < 1) ≈ 0.6827
- P (-2 < Z < 2) ≈ 0.9545
- P (3 < Z < 3) ≈ 0.9973
Given:
μ = 78
σ = 8
<em>X</em> = 62
Compute the distance between the value of <em>X</em> and <em>μ</em> as follows:
Use the relation P (-2 < Z < 2) ≈ 0.9545 to compute the value of P (Z < -2) as follows:
The percentage is, 0.02275 × 100 = 2.275% ≈ 2.3%
Thus, the percent of students who scored below 62 is 2.3%.