Question

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 12.3 and 14.2 years.

Answer 1

To estimate the probability of a meerkat living between 12.3 and 14.2 years, we can use the empirical rule (68-95-99.7%).

Step-by-step explanation:

The probability of a meerkat living between 12.3 and 14.2 years can be estimated using the empirical rule (68-95-99.7%).

1. First, calculate the z-scores for the given values using the formula: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation. For 12.3 years:
   1. z = (12.3 - 10.4) / 1.9 = 0.947
2. For 14.2 years:
   1. z = (14.2 - 10.4) / 1.9 = 2.000

Next, use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores.

1. The probability of a meerkat living less than 12.3 years is the same as the probability of a z-score less than 0.947.
2. The probability of a meerkat living less than or equal to 14.2 years is the same as the probability of a z-score less than or equal to 2.000.

Finally, subtract the probability of the lower value from the probability of the higher value to find the probability of a meerkat living between 12.3 and 14.2 years.

Answer 2

Answer: 13.5 % would be the answer