Question

amy is growing some bean plants. this list represents the current sizes of the plants in centimeters:
\\{7, 7, 8, 8, 8, 9, 9, 11, 12, 15\\}.

should she use a normal curve to represent this data? why or why not?

• no. the data is not evenly distributed. there are more plants below the mean than above the mean.
• yes. the data is not evenly distributed, but its very close. there is almost the same amount of plants below the mean than above the mean.
• yes. the data is evenly distributed. there are the same amount of plants below the mean than above the mean.
• no. he data is not evenly distributed. there are more plants above the mean than below the mean.

Explanation:

Calculate the sample mean

Using the Sample Mean knowledge point, we sum the data values and divide by the total number of observations \(n = 10\):

$$ \text{Sum} = 7 + 7 + 8 + 8 + 8 + 9 + 9 + 11 + 12 + 15 = 94 $$

$$ \text{Mean} = \frac{94}{10} = 9.4 $$

Analyze data distribution relative to the mean

Using the Symmetry Analysis knowledge point, we compare each data point to the calculated mean of \(9.4\):

• Values below the mean (\(< 9.4\)): \(\{7, 7, 8, 8, 8, 9, 9\}\) (7 plants)
• Values above the mean (\(> 9.4\)): \(\{11, 12, 15\}\) (3 plants)

Determine suitability for a normal curve

Using the Normal Distribution Suitability knowledge point, a normal distribution must be symmetric, meaning approximately equal amounts of data should lie on either side of the mean. Here, 7 plants are below the mean and only 3 are above. Thus, the data is not evenly distributed, and there are more plants below the mean than above it.

Answer:

• (A) No. The data is not evenly distributed. There are more plants below the mean than above the mean. (Correct answer)
• (B) Yes. The data is not evenly distributed, but it's very close. There is almost the same amount of plants below the mean than above the mean.
• (C) Yes. The data is evenly distributed. There are the same amount of plants below the mean than above the mean.
• (D) No. he data is not evenly distributed. There are more plants above the mean than below the mean.