Forty-five percent of consumers say it is important that the clothing they buy is made without child labor. You randomly select 

1818 

consumers. Find the probability that the number of consumers who say it is important that the clothing they buy is made without child labor is​ (a) exactly 

sevenseven​, 

​(b) at least 

eleveneleven​, 

and​ (c) less than 

twelvetwelve.

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Part 1

​(a) The probability that the number of consumers who say it is important that the clothing they buy is made without child labor is exactly 

sevenseven 

is 

Upper P left parenthesis exactly seven right parenthesisP(exactly seven)equals=enter your response here.

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

This is a binomial probability problem because we are dealing with a fixed number of trials (1818 consumers), where each trial has two possible outcomes: either a consumer says it is important that the clothing they buy is made without child labor, or they don't. The probability of success (a consumer saying it is important) is given as 45%, or \( p = 0.45 \).

The binomial distribution formula is:

\[
P(X = k) = \binom{n}{k} p^k (1 - p)^{n-k}
\]

Where:
- \( P(X = k) \) is the probability of having exactly \( k \) successes (in this case, 7 consumers),
- \( n = 1818 \) is the number of trials (the number of consumers),
- \( p = 0.45 \) is the probability of success (a consumer who says it is important),
- \( k \) is the number of successes (in this case, 7).

For part (a), we need to calculate the probability that exactly 7 consumers say it is important. Let me calculate that for you.The probability of exactly 7 consumers out of 1818 saying that it is important that the clothing they buy is made without child labor is effectively 0. This result is expected because, with such a large sample size (1818), the probability of exactly 7 successes is extremely small.

Now, let's move on to parts (b) and (c).

Would you like to continue with the calculations for at least 11 and less than 12, or need more details on part (a)? Let me know!

Forty-five percent of consumers say it is important that the clothing they buy is made without child labor. You randomly select 1818 consumers. Find the probability that the number of consumers who say it is important that the clothing they buy is made without child labor is (a) exactly seven, (b) at least eleven, and (c) less than twelve.

Find the probability that exactly 7, at least 11, or less than 12 out of 1818 consumers believe it's important that clothing is made without child labor. Learn how to apply the binomial probability formula with p = 0.45 and n = 1818. Suitable for advanced high school and college students.

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