Question

15 multiple choice 10 points
a grocery store received three shipments of bags of pineapples: one from farm rodriguez, one from farm pacheco, and one from farm maria santos altagracia hernandez. the distributions of the weight of a bag are unimodal and symmetric for all three shipments. the number of bags and the mean and standard - deviation, in ounces (oz), for each shipment are shown in the table.

farm	number of bags	mean (μ)	standard deviation (σ)
pacheco	150	19.0	2
maria santos altagracia hernandez	150	19.0	2

which of the following statements is true?
the shipment from farm rodriguez is most likely to have the greatest number of bags that weigh less than 19 oz.
the shipments from all three farms are all likely to have an approximately equal number of bags that weigh less than 19 oz.
the shipment from farm pacheco is most likely to have the greatest number of bags that weigh less than 19 oz.
the shipment from farm maria santos altagracia hernandez is most likely to have the greatest number of bags that weigh less than 19 oz.
the shipments from farms pacheco and maria santos altagracia hernandez are the only shipments that are likely to have an approximately equal number of bags that weigh less than 19 oz.

Explanation:

Step1: Understand normal - distribution properties

Since the distributions are unimodal and symmetric, they are approximately normal. The mean $\mu = 19$ oz for all three farms. In a normal distribution, 50% of the data lies below the mean.

Step2: Analyze the number of bags and standard - deviation

The number of bags for each farm is $n = 150$. For a normal distribution, the proportion of data below the mean is 0.5 regardless of the standard - deviation.

Answer:

The shipments from all three farms are all likely to have an approximately equal number of bags that weigh less than 19 oz.