Answer:
99.7%
Step-by-step explanation:
The lifespans of meerkats in a particular zoo are normally distributed. The average meerkat lives 10.4 years; the standard deviation is 1.9 years.
Use the empirical rule (68−95−99.7%) to estimate the probability of a meerkat living between 4.7 years and 16.1 years
The empirical rule states that almost all data fall within three standard deviations of the mean for a normal distribution. These are:
-
68% of data falls within the first standard deviation from the mean ( μ ± σ)
- 95% fall within two standard deviations ( μ ± 2σ)
- 99.7% fall within three standard deviations( μ ± 3σ)
Given that:
mean (μ) = 10.4 years and standard deviation σ = 1.9 years
The first standard deviation ( μ ± σ) = (10.4 ± 1.9) = (8.5, 12,4). Therefore, 68% of data falls between 8.5 years and 12.4 years
The second standard deviation ( μ ± 2σ) = (10.4 ± 2×1.9) = (6.6, 14.2). Therefore, 95% of data falls between 6.6 years and 14.2 years
The third standard deviation ( μ ± 3σ) = (10.4 ± 3×1.9) = (4.7, 16.1). Therefore, 99.7% of data falls between 4.7 years and 16.1 years
