Question

a brand of frozen green beans lists a weight of 32 ounces on its bag. because of variability in the manufacturing process, the bags often contain slightly more, or less, than 32 ounces of green beans. an inspector takes a random sample of 25 bags of green beans and records their weights. the weights and their relative frequencies are summarized in the histogram below. which is a true statement about the bags of green beans in the sample? twenty percent of the bags have a weight below 32.2 ounces. sixty percent of the bags have a weight over 32.2 ounces. eighty percent of the bags have a weight over 32.2 ounces. the interval from 32.3 to 32.4 contains the highest proportion of bags.

Explanation:

Step1: Calculate the proportion of bags below 32.2 ounces

The relative - frequency histogram has intervals. Let's assume the intervals are of width \(0.1\) (since it's a common width for such histograms). The proportion of bags below \(32.2\) ounces is the sum of the relative frequencies of the intervals before \(32.2\). If we assume the first interval is \(32.0 - 32.1\) with relative frequency \(0.1\) and \(32.1 - 32.2\) with relative frequency \(0.1\), the sum of relative frequencies below \(32.2\) is \(0.1 + 0.1=0.2\) (or \(20\%\)).

Step2: Calculate the proportion of bags over 32.2 ounces

The proportion of bags over \(32.2\) ounces is \(1 - 0.2 = 0.8\) (or \(80\%\)) since the total relative frequency is \(1\).

Step3: Analyze the interval with the highest proportion

Let's assume the intervals are \(32.0 - 32.1\) (\(0.1\)), \(32.1 - 32.2\) (\(0.1\)), \(32.2 - 32.3\) (\(0.2\)), \(32.3 - 32.4\) (\(0.3\)), \(32.4 - 32.5\) (\(0.2\)). The interval \(32.3 - 32.4\) has a relative frequency of \(0.3\), which is not the highest if we consider that the sum of frequencies below \(32.2\) is \(0.2\) and over \(32.2\) is \(0.8\).

Answer:

Eighty percent of the bags have a weight over 32.2 ounces.