Answer: The problem states that the proportion of people who throw away a portion of what they buy at the grocery store is p = 0.4. We want to find the probability that the sample proportion exceeds a certain value, which we will denote as p-hat.
The sample size is n = 100, which is large enough to use the normal approximation to the binomial distribution.
The formula for the standard error of the sample proportion is:
SE = sqrt[p * (1 - p) / n]
Substituting the values given in the problem, we get:
SE = sqrt[0.4 * 0.6 / 100] = 0.049
To find the z-score corresponding to a sample proportion of , we use the formula:
z = (p-hat - p) / SE
Substituting the values given in the problem, we get:
z = ( - 0.4) / 0.049 = -2.04
Using a standard normal table, we find that the probability of obtaining a z-score of -2.04 or lower is 0.0207. Therefore, the probability that the sample proportion exceeds is approximately 0.0207, rounded to three decimal places.
Explanation: