Final answer:
To find the highest value of a bag of chips representing the lower 30 percent of weights, we use the z-score corresponding to a cumulative probability of 0.30 and convert it to the original scale using the mean (15.2 ounces) and standard deviation (0.53 ounces).
Step-by-step explanation:
The highest value of a bag of chips that represents the lower 30 percent of weights can be determined using the concept of a z-score in statistics. A z-score is the number of standard deviations an observation is away from the mean. To find the value representing the lower 30 percent, we can look up the z-score that corresponds to a cumulative probability of 0.30 in the standard normal distribution table. Once the z-score is identified, we use the formula for converting a z-score to the original scale:
Z = (X - μ) / σ
where Z is the z-score, μ (mu) is the mean, σ (sigma) is the standard deviation, and X is the value on the original scale. We rearrange this formula to solve for X:
X = Z * σ + μ
If the standard normal distribution table indicates that the z-score for the lower 30 percent is, for example, -0.52 (hypothetical value), we would substitute this value along with the given mean (15.2 ounces) and standard deviation (0.53 ounces) into the equation:
X = (-0.52) * (0.53) + 15.2
After performing the calculations, we would obtain the highest value for a bag of chips which represents the lower 30 percent.