Final answer:
To find the probability that the sample proportion of grocery shoppers who throw away part of what they purchase is less than or equal to 0.14, we can use the normal approximation to calculate the z-score and then determine the probability from the standard normal distribution.
Step-by-step explanation:
You asked about the probability that the sample proportion of grocery shoppers who throw away part of what they buy does not exceed 0.14, given that the true proportion is 0.07 according to a 2009 Reader's Digest article. To answer this, we need to understand the sampling distribution of the sample proportion.
Since the sample size is large enough, we can use the normal approximation to the binomial distribution. To find the probability, we calculate the z-score using the formula Z = (p - P) / (sqrt(P(1 - P) / n)), where p is the sample proportion, P is the population proportion, and n is the sample size.
For your question:
- P = 0.07 (true population proportion)
- p = 0.14 (sample proportion of interest)
- n = 74 (sample size)
Calculate the z-score, and then use the standard normal distribution to find the probability that the z-score is less than or equal to the calculated value.
This approach will give you the probability required for your question. Note that if p = 0.14 is the maximum value for which you're trying to find the probability, then the sample proportion of interest you're comparing against is actually any value less than or equal to 0.14.
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