Question

The mean weight of a sample of 250 one-pound bags of plain M&Ms is 16.2 oz. with a standard deviation of 0.1 oz. The dats set is symmetric and mound-shaped. One of the bags had a weight of 16.55 oz. Find the Z-score of this bag, and interpret this value in the context of this data set.

Answer 1

The Z-score for the bag weighing 16.55 oz is 3.5, which means it is 3.5 standard deviations above the mean weight. This indicates that the bag is significantly heavier than the average one-pound bag of plain M&Ms in the sample.

Step-by-step explanation:

To calculate the Z-score of the bag that weighs 16.55 oz, we'll use the formula for the Z-score which is Z = (X - μ) / σ, where X is the value in the dataset, μ (mu) is the mean, and σ (sigma) is the standard deviation. For the given bag, we have:

• X = 16.55 oz (weight of the bag)
• μ = 16.2 oz (mean weight of the bags)
• σ = 0.1 oz (standard deviation)

Plugging these values into the formula gives us:

Z = (16.55 - 16.2) / 0.1

Z = 0.35 / 0.1

Z = 3.5

The Z-score of 3.5 indicates that the weight of this particular bag is 3.5 standard deviations above the mean. In the context of this data set, this bag is significantly heavier than the average bag.