A factory packages mixed nuts made with only almonds and cashews. In one container of

Question

7500
mixed nuts,
2175
of them are almonds and
5325
of them are cashews.

(a)Construct a percent bar graph for the mixed nuts in the container.

50%50%
AlmondsCashews

Let's simulate three random samples of
125
mixed nuts from the container. Press all three "Run" buttons to do so. (You can press "Run" multiple times to generate more samples to see how they vary.)
Run
Run

Sample size:
0
Number
%
of totalAlmonds
Cashews
Run
Run

Sample size:
0
Number
%
of totalAlmonds
Cashews
Run
Run

Sample size:
0
Number
%
of totalAlmonds
Cashews
(b)In part (a), we calculated two different types of percentages: population percentages in the percent bar graph and sample percentages in the simulations.
The almond population percentage is the percentage of the
7500
mixed nuts that are almonds.
The almond sample percentage is the percentage of mixed nuts that are almonds in a random sample of
125
mixed nuts.
True or false?
StatementTrueFalseAny random sample of
125
mixed nuts will always have
62
almonds.
In any random sample of
125
mixed nuts, the almond sample percentage must always be equal to the almond population percentage.
With a very large sample size, there might be a difference between the almond sample percentage and the almond population percentage, but the difference should be small.

Answer 1

Let's break down the questions step by step.

(a) Percent Bar Graph for Mixed Nuts

You mentioned there are 2175 almonds and 5325 cashews in a total of 7500 mixed nuts. To create a percent bar graph, we first need to calculate the percentage of almonds and cashews:

1. Percentage of almonds: \[ \text{Percentage of almonds} = \left( \frac{2175}{7500} \right) \times 100 = 29% \]

2. Percentage of cashews: \[ \text{Percentage of cashews} = \left( \frac{5325}{7500} \right) \times 100 = 71% \]

Based on this calculated data, the percent bar graph would look something like:

• Almonds: 29%
• Cashews: 71%

(b) Statements Regarding Random Samples

Now, let’s evaluate the statements you're asking about:

1. Statement: "Any random sample of 125 mixed nuts will always have 62 almonds."

   • True or False? False
   • Reason: The number of almonds in any sample of 125 mixed nuts is random. While on average, we might expect around 62 almonds based on the population percentage (29% of 125 is indeed about 36.25), the actual count can vary.

2. Statement: "In any random sample of 125 mixed nuts, the almond sample percentage must always be equal to the almond population percentage."

   • True or False? False
   • Reason: The almond sample percentage can vary since it depends on the random selection of mixed nuts. It is unlikely to match the population percentage exactly in every sample.

3. Statement: "With a very large sample size, there might be a difference between the almond sample percentage and the almond population percentage, but the difference should be small."

   • True or False? True
   • Reason: As sample size increases, according to the Law of Large Numbers, the sample percentages should converge to the population percentages, resulting in a smaller difference. However, while the difference can become small, it might not necessarily become zero.

Let me know if you need further information on any of these points!