Math / Data & Statistics

QuestionMatch each of the normal curves to its mean $\mu$ and standard deviation $\sigma$ .
Part 1 of 2 (a)
Normal curve with $\square$ (Choose one) $\begin{array}{ll} \mu=4, & \sigma=1 \\ \mu=4, & \sigma=3 \end{array}$

Studdy Solution

STEP 1

What is this asking? We need to figure out which mean ( $\mu$ ) and standard deviation ( $\sigma$ ) describe the given normal distribution curve. Watch out! Don't mix up mean and standard deviation!
The mean tells us where the center of the curve is, while the standard deviation tells us how spread out it is.

STEP 2

1. Analyze the curve's center.
2. Analyze the curve's spread.

STEP 3

Alright, let's locate the center of our bell curve!
It's the highest point on the curve, right?
Looking at the graph, the peak of the curve sits right at $x = 0$ .
This means our mean ( $\mu$ ) is 0.

STEP 4

Now, let's look at how spread out the curve is.
A narrow curve means a small standard deviation, while a wide curve means a large standard deviation.

STEP 5

The problem gives us two options: $\sigma = 1$ or $\sigma = 3$ .
Since the curve is quite narrow and concentrated around the mean, it suggests a smaller standard deviation.

STEP 6

The image description says the curve has a "narrow peak indicating a small standard deviation".
This confirms that the standard deviation ( $\sigma$ ) is 1.

STEP 7

The normal curve has a mean ( $\mu$ ) of 0 and a standard deviation ( $\sigma$ ) of 1.
Since the problem only provided options for a mean of 4, and we've determined the mean is 0, neither of the provided options are correct.

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QuestionMatch each of the normal curves to its mean $\mu$ and standard deviation $\sigma$ .
Part 1 of 2 (a)
Normal curve with $\square$ (Choose one) $\begin{array}{ll} \mu=4, & \sigma=1 \\ \mu=4, & \sigma=3 \end{array}$

Studdy Solution

STEP 1

STEP 2

1. Analyze the curve's center.
2. Analyze the curve's spread.

STEP 3

Alright, let's locate the center of our bell curve!
It's the highest point on the curve, right?
Looking at the graph, the peak of the curve sits right at $x = 0$ .
This means our mean ( $\mu$ ) is 0.

STEP 4

Now, let's look at how spread out the curve is.
A narrow curve means a small standard deviation, while a wide curve means a large standard deviation.

STEP 5

The problem gives us two options: $\sigma = 1$ or $\sigma = 3$ .
Since the curve is quite narrow and concentrated around the mean, it suggests a smaller standard deviation.

STEP 6

The image description says the curve has a "narrow peak indicating a small standard deviation".
This confirms that the standard deviation ( $\sigma$ ) is 1.

STEP 7

The normal curve has a mean ( $\mu$ ) of 0 and a standard deviation ( $\sigma$ ) of 1.
Since the problem only provided options for a mean of 4, and we've determined the mean is 0, neither of the provided options are correct.

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QuestionMatch each of the normal curves to its mean μ\muμ and standard deviation σ\sigmaσ.Part 1 of 2 (a)Normal curve with □\square□ (Choose one) μ=4,σ=1μ=4,σ=3\begin{array}{ll} \mu=4, & \sigma=1 \\ \mu=4, & \sigma=3 \end{array}μ=4,μ=4,​σ=1σ=3​

Studdy Solution

STEP 1

STEP 2

1. Analyze the curve's center.2. Analyze the curve's spread.

STEP 3

Alright, let's **locate the center** of our bell curve!It's the highest point on the curve, right?Looking at the graph, the peak of the curve sits right at x=0x = 0x=0.This means our **mean** (μ\muμ) is **0**.

STEP 4

Now, let's look at how **spread out** the curve is.A narrow curve means a small standard deviation, while a wide curve means a large standard deviation.

STEP 5

The problem gives us two options: σ=1\sigma = 1σ=1 or σ=3\sigma = 3σ=3.Since the curve is quite narrow and concentrated around the mean, it suggests a **smaller standard deviation**.

STEP 6

The image description says the curve has a "narrow peak indicating a small standard deviation".This confirms that the **standard deviation** (σ\sigmaσ) is **1**.

STEP 7

The normal curve has a **mean** (μ\muμ) of **0** and a **standard deviation** (σ\sigmaσ) of **1**.Since the problem only provided options for a mean of 4, and we've determined the mean is 0, neither of the provided options are correct.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionMatch each of the normal curves to its mean $\mu$ and standard deviation $\sigma$ .
Part 1 of 2 (a)
Normal curve with $\square$ (Choose one) $\begin{array}{ll} \mu=4, & \sigma=1 \\ \mu=4, & \sigma=3 \end{array}$

1. Analyze the curve's center.
2. Analyze the curve's spread.

Alright, let's locate the center of our bell curve!
It's the highest point on the curve, right?
Looking at the graph, the peak of the curve sits right at $x = 0$ .
This means our mean ( $\mu$ ) is 0.

Now, let's look at how spread out the curve is.
A narrow curve means a small standard deviation, while a wide curve means a large standard deviation.

The problem gives us two options: $\sigma = 1$ or $\sigma = 3$ .
Since the curve is quite narrow and concentrated around the mean, it suggests a smaller standard deviation.

The image description says the curve has a "narrow peak indicating a small standard deviation".
This confirms that the standard deviation ( $\sigma$ ) is 1.

The normal curve has a mean ( $\mu$ ) of 0 and a standard deviation ( $\sigma$ ) of 1.
Since the problem only provided options for a mean of 4, and we've determined the mean is 0, neither of the provided options are correct.