Answer:
16%
Step-by-step explanation:
The Empirical rule formula states that:
a) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .
b) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ
From the question, we have:
sample mean height = 64.3 inches sample standard deviation of s = 2.4 inches,
Imputing that into the first Empirical rule,
a) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .
μ = 64.3 inches
σ = 2.4 inches
64.3 + 2.4 = 67.7 inches
64.3 - 2.4 = 61.9 inches
Hence, from the above calculation, 68% of the data have 61.9 inches as their height.
We are to find the percentage that falls below 61.9 inches
= 100 - % of those that fall within 61.9 inches
= 100% - 68 %
= 32%
Since we have two sides for a distribution,
= 32%/2
= 16 %
Therefore, the percentage of those that fall below 61.9 inches is 16%
