Returning to the sample of adult women, with a sample mean height of x¯=64.3 inches and sample standard deviation of s=2.4 inches, use the Empirical Rule to estimate the percentage of heights that are less than 61.9 inches.

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%

2

step-by-2step explanation: