To solve the problem using the empirical rule, we first need to clarify and fill in some missing details. However, I will present the solution structure based on what is typically required in such problems.

### 1. Break Down the Problem
1. Identify the mean lifespan of the gorilla.
2. Identify the standard deviation of the gorilla's lifespan.
3. Determine the lifespan for which we need to calculate the probability (greater than a specific age).

### 2. Relevant Concepts
- The empirical rule states:
- Approximately 68% of the data falls within 1 standard deviation of the mean.
- Approximately 95% of the data falls within 2 standard deviations of the mean.
- Approximately 99.7% of the data falls within 3 standard deviations of the mean.

### 3. Analysis and Detail
Let:
- $ \mu $ = mean lifespan of the gorilla (in years)
- $ \sigma $ = standard deviation of lifespan (in years)
- $ X $ = age threshold we are evaluating against

To determine the probability of a gorilla living longer than $ X $:
1. Calculate the number of standard deviations $ z $ that $ X $ is away from the mean:
$$
z = \frac{X - \mu}{\sigma}
$$

2. Use the standard normal distribution to find the corresponding probability related to that $ z $-score.

### 4. Verify and Summarize
1. Ensure the calculations are performed accurately.
2. Summarize the probability found for $ P(X \text{Age}) $.

### Final Answer
Given the mean and standard deviation, the final result will depend on the specific values, which were not provided. However, once those values are inserted, the probability can be calculated and displayed in the final answer. For example:
- If $ \mu = 20 $ years, $ \sigma = 5 $ years, and $ X = 25 $ years:
$$
z = \frac{25 - 20}{5} = 1
$$
Using standard normal distribution tables or calculators, determine $ P(Z 1) $ which leads to the final probability.

For the actual calculation, please provide the specific values for mean, standard deviation, and the given age threshold.

Question

To solve the problem using the empirical rule, we first need to clarify and fill in some missing details. However, I will present the solution structure based on what is typically required in such problems.

### 1. Break Down the Problem
1. Identify the mean lifespan of the gorilla.
2. Identify the standard deviation of the gorilla's lifespan.
3. Determine the lifespan for which we need to calculate the probability (greater than a specific age).

### 2. Relevant Concepts
- The empirical rule states:
  - Approximately 68% of the data falls within 1 standard deviation of the mean.
  - Approximately 95% of the data falls within 2 standard deviations of the mean.
  - Approximately 99.7% of the data falls within 3 standard deviations of the mean.

### 3. Analysis and Detail
Let:
- $ \mu $ = mean lifespan of the gorilla (in years)
- $ \sigma $ = standard deviation of lifespan (in years)
- $ X $ = age threshold we are evaluating against

To determine the probability of a gorilla living longer than $ X $:
1. Calculate the number of standard deviations $ z $ that $ X $ is away from the mean:
   $$
   z = \frac{X - \mu}{\sigma}
   $$

2. Use the standard normal distribution to find the corresponding probability related to that $ z $-score.

### 4. Verify and Summarize
1. Ensure the calculations are performed accurately.
2. Summarize the probability found for $ P(X > \text{Age}) $.

### Final Answer
Given the mean and standard deviation, the final result will depend on the specific values, which were not provided. However, once those values are inserted, the probability can be calculated and displayed in the final answer. For example:
- If $ \mu = 20 $ years, $ \sigma = 5 $ years, and $ X = 25 $ years:
  $$
  z = \frac{25 - 20}{5} = 1
  $$
Using standard normal distribution tables or calculators, determine $ P(Z > 1) $ which leads to the final probability.

For the actual calculation, please provide the specific values for mean, standard deviation, and the given age threshold.

Knowee AI · Accepted Answer