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 longer than \[16.1\] years.

\[\%\]

You want to use the empirical rule to estimate the probability a meerkat will live longer than 16.1 years if the population has a normally-distributed lifespan with mean 10.4 years and standard deviation 1.9 years.

Z-score

The number of standard deviations away from the mean represented by 16.1 years is ...

[tex]Z = \dfrac{X-\mu}{\sigma}=\dfrac{16.1-10.4}{1.9}=3[/tex]

Empirical rule

The empirical rule tells us that the middle 99.7% of the distribution lies within 3 standard deviations of the mean. The remaining 0.3% is equally distributed between the two tails of the distribution. This means the probability of interest is ...

P(Z>3) ≈ (1 -0.997)/2 = 0.0015 = 0.15%

The probability a meerkat will live longer than 16.1 years is about 0.15%.

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 longer than \[16.1\] years. \[\%\]

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Z-score

Empirical rule

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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 longer than \[16.1\] years.

\[\%\]