b) The probability that 

eighteight 

randomly selected 

11​-year-old 

male 

stink bugstink bugs 

will live to be 

22 

years old is 

0.698340.69834.

​(Round to five decimal places as​ needed.)

Yes, let's round the probability to five decimal places as needed.

Given that the calculation for eight randomly selected 1-year-old male stink bugs is:

\[ P(\text{all survive}) = 0.95208^8 \]

We calculated it as:

\[ P(\text{all survive}) \approx 0.698337 \]

When rounded to five decimal places, the probability is:

\[ P(\text{all survive}) \approx 0.69834 \]

So, the probability that eight randomly selected 1-year-old male stink bugs will live to be 2 years old is \( 0.69834 \).

Would you like more details or have any questions? Here are some other questions you might want to explore:

1. What is the probability that exactly one out of two stink bugs will live to be 2 years old?
2. How would the probabilities change if the survival rate was different?
3. What is the probability that at least one out of eight stink bugs will not live to be 2 years old?
4. How can we generalize the formula for any number of stink bugs?
5. What are the real-world applications of these probability calculations?

**Tip:** Always check your calculations and rounding carefully, especially when dealing with probabilities, as small differences can significantly impact the results.

Explore the probability calculation for the survival of eight randomly selected 1-year-old male stink bugs to be 2 years old. The solution involves calculating the probability of all bugs surviving, rounding to five decimal places, and understanding implications for survival analysis.

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