22% of adults would pay more for environmentally friendly products. You randomly select 10 adults. Find the probability that the number of adults who would pay more for environmentally friendly products is (a) exactly two, and (b) between two and five, inclusive. (a) P(2)=(Round to the nearest thousandth as needed.) (b)P(2

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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**Text Transcription for Educational Website:**

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**Problem Statement:**

22% of adults would pay more for environmentally friendly products. You randomly select 10 adults. Find the probability that the number of adults who would pay more for environmentally friendly products is (a) exactly two, and (b) between two and five, inclusive.

**Tasks:**

(a) Calculate P(2) = □ (Round to the nearest thousandth as needed.)

(b) Calculate P(2 ≤ x ≤ 5) = □ (Round to the nearest thousandth as needed.)

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**Explanation:**

The problem involves calculating probabilities for a binomial distribution where the probability of success (an adult willing to pay more) is 22%, and the number of trials is 10. 

- In part (a), you are required to find the probability that exactly 2 adults out of 10 would pay more for environmentally friendly products.
- In part (b), you need to find the probability that between 2 and 5 adults (inclusive) would pay more.

These calculations typically require the use of a binomial probability formula or distribution table. Rounding should be done to three decimal places.
Transcribed Image Text:**Text Transcription for Educational Website:** --- **Problem Statement:** 22% of adults would pay more for environmentally friendly products. You randomly select 10 adults. Find the probability that the number of adults who would pay more for environmentally friendly products is (a) exactly two, and (b) between two and five, inclusive. **Tasks:** (a) Calculate P(2) = □ (Round to the nearest thousandth as needed.) (b) Calculate P(2 ≤ x ≤ 5) = □ (Round to the nearest thousandth as needed.) --- **Explanation:** The problem involves calculating probabilities for a binomial distribution where the probability of success (an adult willing to pay more) is 22%, and the number of trials is 10. - In part (a), you are required to find the probability that exactly 2 adults out of 10 would pay more for environmentally friendly products. - In part (b), you need to find the probability that between 2 and 5 adults (inclusive) would pay more. These calculations typically require the use of a binomial probability formula or distribution table. Rounding should be done to three decimal places.
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