**Educational Content on Z-Scores and Normal Distribution**---**Sketching the Z-Score Graph**To understand z-scores, it's essential to visualize them on the normal distribution curve. Here's a step-by-step guide to help you sketch the z-score with the area of interest and then find the specific z-score.**Links to Resources:**- [Page 1 of the Normal Distribution Table](#)- [Page 2 of the Normal Distribution Table](#)**Task (a): Determine $ Z_{0.04} $**1. **Graph Selection:** - You're asked to sketch the graph that represents $ Z_{0.04} $. Choose the correct graph from the options below which show the z-score on a normal distribution curve. - **Options:** - **A:** Histogram with a highlighted section of the curve starting from the left. - **B:** Normal curve with a small shaded area at the left. - **C:** Normal curve with a shaded area at the far right. - **D:** Normal curve with a shaded area on the right side, indicating the area of interest with a probability of 0.04. - The correct choice is **D**, which accurately shows the area of interest with 0.04 shaded on the right of the curve.2. **Determining $ Z_{0.04} $:** - The z-score $ Z_{0.04} $ is calculated, and the result is 0.89. This z-value corresponds to the point on the normal distribution curve where the area to the right is 0.04. - **Formula Used:** - The normal distribution table is used to find the z-score that leaves 4% in the tail, resulting in: \[ Z_{0.04} = 0.89 \quad (\text{round to two decimal places as needed}) \]Following these steps ensures you understand how to visualize and calculate z-scores on a normal distribution curve, enhancing your statistical analysis skills. **Normal Distribution and Z-Scores****Sketch the graph that shows $ z_{0.34} $ and then determine $ z_{0.34}^* $.**- **Click here to view page 1 of the normal distribution table.**- **Click here to view page 2 of the normal distribution table.****Choose the correct graph below.**- **Option A:** A normal distribution curve with an area of 0.34 shaded to the right of $ z_{0.34} $.- **Option B:** A normal distribution curve with an area of 0.34 shaded to the left of $ z_{0.34} $.- **Option C:** A normal distribution curve with two tails shaded, each with an area of 0.34, symmetrically around zero, reaching up to $ -z_{0.34} $ and $ z_{0.34} $. *(Correct choice)*- **Option D:** A normal distribution curve with a central area of 0.34 shaded around zero.**Now determine $ z_{0.34}^* $:**- $ z_{0.34} = \boxed{0.98} $ (Round to two decimal places as needed.)

Name: **Educational Content on Z-Scores and Normal Distribution**---**Sketc
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Description: **Educational Content on Z-Scores and Normal Distribution**---**Sketching the Z-Score Graph**To understand z-scores, it's essential to visualize them on the normal distribution curve. Here's a step-by-step guide to help you sketch the z-score with t

Sketch the normal curve and shade the area of 0.04 to the right of z. Since the total area under the normal curve is 1. therefore, the area to the left of normal is 1-0.04 = 0.96 Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.96 to the left of the normal curveORUse excel formula "=NORM.S.INV(0.96)" to find the z-score. Therefore, Sketch the normal curve and shade the area of 0.34 to the right of z. Since the total area under the normal curve is 1. therefore, the area to the left of normal is 1-0.34 = 0.66 Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.66 to the left of the normal curveORUse excel formula "=NORM.S.INV(0.66)" to find the z-score. Therefore,

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Sketch the graph that shows the z-score with the area of interest and then find the z-score. Complete parts (a) and (b) below. Click here to view page 1 of the normal distribution table, Click here to view page 2 of the normal distribution table, a. Zo,04 First sketch the graph that shows zo.04. Choose the correct graph below. O A. OB. Oc. OD. Q 0.04 0.04 0.04 0.04 Z0.04 0 Z0.04 6 Z0,04 Z0.04 Now determine z0.04- Z0.04 = 0.89 (Round to two decimal places as needed.)

Sketch the graph that shows the z-score with the area of interest and then find the z-score. Complete parts (a) and (b) below. Click here to view page 1 of the normal distribution table, Click here to view page 2 of the normal distribution table, a. Zo,04 First sketch the graph that shows zo.04. Choose the correct graph below. O A. OB. Oc. OD. Q 0.04 0.04 0.04 0.04 Z0.04 0 Z0.04 6 Z0,04 Z0.04 Now determine z0.04- Z0.04 = 0.89 (Round to two decimal places as needed.)

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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

Topic Video

Question

**Educational Content on Z-Scores and Normal Distribution**

---

**Sketching the Z-Score Graph**

To understand z-scores, it's essential to visualize them on the normal distribution curve. Here's a step-by-step guide to help you sketch the z-score with the area of interest and then find the specific z-score.

**Links to Resources:**
- [Page 1 of the Normal Distribution Table](#)
- [Page 2 of the Normal Distribution Table](#)

**Task (a): Determine $ Z_{0.04} $**

1. **Graph Selection:**

- You're asked to sketch the graph that represents $ Z_{0.04} $. Choose the correct graph from the options below which show the z-score on a normal distribution curve.

- **Options:**
- **A:** Histogram with a highlighted section of the curve starting from the left.
- **B:** Normal curve with a small shaded area at the left.
- **C:** Normal curve with a shaded area at the far right.
- **D:** Normal curve with a shaded area on the right side, indicating the area of interest with a probability of 0.04.

- The correct choice is **D**, which accurately shows the area of interest with 0.04 shaded on the right of the curve.

2. **Determining $ Z_{0.04} $:**

- The z-score $ Z_{0.04} $ is calculated, and the result is 0.89. This z-value corresponds to the point on the normal distribution curve where the area to the right is 0.04.

- **Formula Used:**
- The normal distribution table is used to find the z-score that leaves 4% in the tail, resulting in:
\[
Z_{0.04} = 0.89 \quad (\text{round to two decimal places as needed})
\]

Following these steps ensures you understand how to visualize and calculate z-scores on a normal distribution curve, enhancing your statistical analysis skills.

**Normal Distribution and Z-Scores**

**Sketch the graph that shows $ z_{0.34} $ and then determine $ z_{0.34}^* $.**

- **Click here to view page 1 of the normal distribution table.**
- **Click here to view page 2 of the normal distribution table.**

**Choose the correct graph below.**

- **Option A:** A normal distribution curve with an area of 0.34 shaded to the right of $ z_{0.34} $.
- **Option B:** A normal distribution curve with an area of 0.34 shaded to the left of $ z_{0.34} $.
- **Option C:** A normal distribution curve with two tails shaded, each with an area of 0.34, symmetrically around zero, reaching up to $ -z_{0.34} $ and $ z_{0.34} $. *(Correct choice)*
- **Option D:** A normal distribution curve with a central area of 0.34 shaded around zero.

**Now determine $ z_{0.34}^* $:**

- $ z_{0.34} = \boxed{0.98} $ (Round to two decimal places as needed.)

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