Questions: Consider two normal distributions, one with mean -4 and standard deviation 3.4, and the other with mean 6 and standard deviation 3.4. Answer true or false to each statement and explain your answers. a. The two normal distributions have the same spread. b. The two normal distributions are centered at the same place. a. Choose the correct answer below. A. False because the distributions have different means. B. True because the distributions have the same mean. C. True because the distributions have the same standard deviation. D. False because the distributions have different standard deviations.

Consider two normal distributions, one with mean -4 and standard deviation 3.4, and the other with mean 6 and standard deviation 3.4. Answer true or false to each statement and explain your answers.
a. The two normal distributions have the same spread.
b. The two normal distributions are centered at the same place.
a. Choose the correct answer below.
A. False because the distributions have different means.
B. True because the distributions have the same mean.
C. True because the distributions have the same standard deviation.
D. False because the distributions have different standard deviations.
Transcript text: Consider two normal distributions, one with mean -4 and standard deviation 3.4, and the other with mean 6 and standard deviation 3.4. Answer true or false to each statement and explain your answers. a. The two normal distributions have the same spread. b. The two normal distributions are centered at the same place. a. Choose the correct answer below. A. False because the distributions have different means. B. True because the distributions have the same mean. C. True because the distributions have the same standard deviation. D. False because the distributions have different standard deviations.
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Solution

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Solution Steps

Step 1: Determine the Spread of the Distributions

To determine if the two normal distributions have the same spread, we compare their standard deviations. The standard deviation (\(\sigma\)) measures the spread of a distribution.

Given:

  • Distribution 1: \(\sigma_1 = 3.4\)
  • Distribution 2: \(\sigma_2 = 3.4\)

Since \(\sigma_1 = \sigma_2\), the two distributions have the same spread.

Step 2: Determine the Center of the Distributions

To determine if the two normal distributions are centered at the same place, we compare their means (\(\mu\)).

Given:

  • Distribution 1: \(\mu_1 = -4\)
  • Distribution 2: \(\mu_2 = 6\)

Since \(\mu_1 \neq \mu_2\), the two distributions are not centered at the same place.

Final Answer

a. The two normal distributions have the same spread.
\[ \boxed{\text{True because the distributions have the same standard deviation.}} \]

b. The two normal distributions are centered at the same place.
\[ \boxed{\text{False because the distributions have different means.}} \]

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