Answer:
13.5% probability of a meerkat living between 12.3 and 14.2 years.
Explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 10.4
Standard deviation = 1.9
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above the mean.
Between 12.3 and 14.2 years.
12.3 = 10.4 + 1.9
So 12.3 is one standard deviation above the mean.
50% of the measures are above the mean. Of those, 68% are within 1 standard deviation of the mean.
14.2 = 10.4 + 2*1.9
So 14.2 is two standard deviations above the mean.
50% of the measures are above the mean. Of those, 95% are within 2 standard deviation of the mean.
0.5*0.95 - 0.5*0.68 = 0.135
13.5% probability of a meerkat living between 12.3 and 14.2 years.