The histogram shows the reviewer ratings on a scale from 1 (lowest) to 5 (highest) of a recently published book. Reviewer Ratings 0.435 (a) Find the mean, variance, and standard deviation of the probability distribution. (b) Interpret the results. 0.5- 0.4 0.3- 0.2- 0.1- 0.0- 0.213 0.242 0.090 0.020 4. Probability

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**Educational Website Content**

### Review Analysis of a Recently Published Book

The histogram visualizes the reviewer ratings for a recently published book on a scale from 1 (lowest) to 5 (highest). 

#### Histogram Breakdown

- **X-Axis (Rating):** Represents the ratings from 1 to 5.
- **Y-Axis (Probability):** Shows the probability of each rating.

**Bar Details:**

- Rating 1: Probability of 0.020
- Rating 2: Probability of 0.090
- Rating 3: Probability of 0.213
- Rating 4: Probability of 0.242
- Rating 5: Probability of 0.435

#### Statistical Analysis

**Task:**

(a) **Calculate the mean, variance, and standard deviation of the probability distribution.**

- **The mean** is ___. (Type an integer or a decimal. Do not round.)
  
- **The variance** is ___. (Round to two decimal places as needed.)

- **The standard deviation** is ___. (Round to two decimal places as needed.)

(b) **Interpret the results.** Select all that apply.

- **A.** The typical rating deviates from the mean by about 4.
- **B.** The typical rating deviates from the mean by about 1.
- **C.** The average rating for the book is approximately 4.
- **D.** The average rating for the book is approximately 1. 

Please fill in the blanks with the appropriate calculations and interpretations.
Transcribed Image Text:**Educational Website Content** ### Review Analysis of a Recently Published Book The histogram visualizes the reviewer ratings for a recently published book on a scale from 1 (lowest) to 5 (highest). #### Histogram Breakdown - **X-Axis (Rating):** Represents the ratings from 1 to 5. - **Y-Axis (Probability):** Shows the probability of each rating. **Bar Details:** - Rating 1: Probability of 0.020 - Rating 2: Probability of 0.090 - Rating 3: Probability of 0.213 - Rating 4: Probability of 0.242 - Rating 5: Probability of 0.435 #### Statistical Analysis **Task:** (a) **Calculate the mean, variance, and standard deviation of the probability distribution.** - **The mean** is ___. (Type an integer or a decimal. Do not round.) - **The variance** is ___. (Round to two decimal places as needed.) - **The standard deviation** is ___. (Round to two decimal places as needed.) (b) **Interpret the results.** Select all that apply. - **A.** The typical rating deviates from the mean by about 4. - **B.** The typical rating deviates from the mean by about 1. - **C.** The average rating for the book is approximately 4. - **D.** The average rating for the book is approximately 1. Please fill in the blanks with the appropriate calculations and interpretations.
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