1. **Stating the problem:**
We are given that the probability a randomly selected U.S. adult drinks coffee on a given day is $0.56$.
2. **Explain what this probability means:**
The probability $0.56$ means that if you randomly pick one U.S. adult, there is a 56% chance that this person drinks coffee on that day. It is a measure of likelihood, not a guarantee.
3. **If a researcher surveys 100 U.S. adults, will exactly 56 have consumed coffee?**
No, not necessarily. The number 56 is the expected value (mean) of coffee drinkers in a sample of 100 adults, calculated as:
$$\text{Expected number} = 100 \times 0.56 = 56$$
4. **Why not exactly 56?**
Because the actual number of coffee drinkers in the sample follows a binomial distribution with parameters $n=100$ and $p=0.56$. The number can vary around 56 due to randomness.
5. **Summary:**
- Probability $0.56$ means 56% chance for any one adult.
- In 100 adults, the average number drinking coffee is 56.
- The exact number can be more or less than 56 in any particular survey.
Coffee Probability 75Acc2
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