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. A histogram titled 'Green Beans' has actual weight (ounces) on the x-axis and relative frequency on the y-axis. The intervals and their relative frequencies are as follows: 31.8 to 31.9, 0.04; 31.9 to 32.0, 0.04; 32.0 to 32.1, 0.12; 32.1 to 32.2, 0.2; 32.2 to 32.3, 0.36; 32.3 to 32.4, 0.23. Which of the following statements about the bags of green beans in the sample is true?

1) Twenty percent of the bags have a weight below 32.2 ounces.
2) Sixty percent of the bags have a weight over 32.2 ounces.
3) Eighty percent of the bags have a weight over 32.2 ounces.
4) The interval from 32.3 to 32.4 contains the highest proportion of bags.

Answer 1

The histogram shows that the interval from 32.3 to 32.4 contains the highest proportion of bags of green beans.

Step-by-step explanation:

The histogram shows the weights of 25 bags of frozen green beans. From the histogram, we can observe that the highest proportion of bags falls within the interval from 32.2 to 32.3 ounces, as it has a relative frequency of 0.36.

Therefore, the statement that is true is that the interval from 32.3 to 32.4 contains the highest proportion of bags.

It is important to note that none of the given statements provide information about the proportion of bags with a weight below or above 32.2 ounces, so statements 1, 2, and 3 are not supported by the information provided in the histogram.