Answer:
Explanation:
The question is incomplete. The complete question is:
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
Solution:
Let x be a random variable representing the lifespans of meerkats in a particular zoo. With the mean and standard deviation given, then the Empirical Rule says the that
1) About 68% of the x values lie between 1 standard deviation below and above the mean.
2) About 95% of the x values lie between 2 standard deviations below and above the mean.
3) About 99.7% of the x values lie between 3 standard deviations below and above the mean.
From the information given,
mean = 10.4 years
Standard deviation = 1.9 years
x = 16.1 years
Therefore,
3 standard deviations = 3 × 1.9 = 5.7 years
16.1 = 10.4 ± 5.7
Therefore, x is 3 standard deviations from the mean. Therefore, the probability of a meerkat living longer than 16.1 is 99.7%