Answer:
0.9985
Explanation:
You want the probability that a meerkat will live less than 16.1 years if their lifespan is normally distributed with mean 10.4 years and standard deviation 1.9 years.
Z-score
The z-score of the longevity is ...
(16.1 -10.4)/1.9 = 3
The empirical rule tells us that the central 3 standard deviations from the mean enclose 99.7% of the distribution. Half the remaining distribution will lie below -3 standard deviations from the mean. This tells us that the desired probability is ...
P(Z < 3) ≈ 0.997 +0.003/2 = 0.9985
The probability a meerkat lives less than 16.1 years is estimated to be 0.9985.
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