Question

Finding Binomial Probabilities In Exercises 19–26, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B.

Responsible Consumption Forty-five percent of consumers say it is important that the clothing they buy is made without child labor. You randomly select 16 consumers. Find the probability that the number of of consumers who say it is important that the clothing they buy is made without child labor is (a) e

Accepted Answer

Step 1: Identify the problem type. This is a binomial probability problem because we are dealing with a fixed number of trials (16 consumers), two possible outcomes (say it is important or not), and a constant probability of success (45% or 0.45). Step 2: Define the binomial random variable. Let X represent the number of consumers who say it is important that the clothing they buy is made without child labor. X follows a binomial distribution with parameters n = 16 (number of trials) and p = 0.45 (probability of success). Step 3: Write the formula for the binomial probability. The probability mass function for a binomial random variable is given by: P(X=k)=(n!k!(n-k)!)&#xD7;pk&#xD7;(1-p)n-k, where k is the number of successes, n is the number of trials, and p is the probability of success. Step 4: Plug in the values for n and p into the formula. For this problem, n = 16 and p = 0.45. To find the probability for a specific value of k (the number of successes), substitute k into the formula and calculate the result. Step 5: Use technology or a binomial probability table to compute the probability for the desired value of k. If using technology, such as a calculator or statistical software, input the values for n, p, and k to obtain the probability. Alternatively, refer to Table 2 in Appendix B for the binomial probabilities.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Binomial Distribution

Probability Mass Function (PMF)

Cumulative Probability