i keep getting these wrong, can someone explain how to solve? **Bus Departure Time Distribution**The time (in minutes) until the next bus departs a major bus depot follows a uniform distribution with $ f(x) = \frac{1}{20} $, where $ x $ ranges from 25 to 45 minutes.**Problem:**Find the probability that the time is between 35 and 40 minutes. (Enter your answer as a fraction.)**Visual Explanation:**Four histograms are provided to represent the uniform distribution:1. **Histogram 1:** - **Y-axis:** $ f(x) $ ranging from 0 to 0.20 - **X-axis:** Time from 0 to 50 minutes - **Shaded Area:** Between 35 and 40 minutes - **Description:** This plot highlights the uniform distribution where the area of interest is the shaded region between 35 and 40.2. **Histogram 2:** - Similar structure as Histogram 1 - Provides a visual focus on the shaded probability area between 35 and 40.3. **Histogram 3:** - Shows the full distribution curve with emphasis on the complete area of interest between 25 and 45 minutes. - The same shaded region for probabilities between 35 and 40.4. **Histogram 4:** - Shows a cumulative probability distribution. - Shaded area illustrates cumulative probabilities up to 40 minutes.Upon solving, you will find the probability by calculating the area of the shaded region in proportion to the entire distribution.**Probability Calculation:**Write the answer as a probability statement, indicating the probability that a waiting time between 35 and 40 minutes occurs, given the specified uniform distribution. **Educational Content:****Distribution Analysis for Bus Departure Times**The time (in minutes) until the next bus departs a major bus depot follows a uniform distribution, given by the probability density function:\[ f(x) = \frac{1}{20} \]This function is valid for $x$ ranging from 25 to 45 minutes.**Objective:**Find the probability that the time is between 35 and 40 minutes.**Solution Steps:**1. **Calculate the Probability:** - To find the probability that the bus departs between 35 and 40 minutes, integrate the probability density function $f(x)$ over this interval.2. **Graphical Representation:** - The graph of the uniform distribution is a horizontal line at $f(x) = 0.05$ from $x = 25$ to $x = 45$. The area of interest (35 to 40 minutes) is shaded on this graph.3. **Graph Explanation:** - **First Graph:** Displays the uniform distribution from 0 to 50 minutes, with a focus between 35 and 40 minutes. - **Second Graph:** Highlights the same interval with markings to show the probability density function value. - **Third Graph:** Demonstrates the uniform distribution again, indicating the continuous nature of the probability distribution.**Probability Statement:**- Use the graphical representation and integration to confirm the probability related to the range of interest.- Complete the sentence: "The probability of a waiting time between 35 and 40 minutes is $\frac{1}{4}$, given waiting times from 25 to 45 minutes."This overview helps in understanding the application of uniform distributions to real-world situations, such as predicting bus departure times.

Name: i keep getting these wrong, can someone explain how to solve? **Bus De
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Description: i keep getting these wrong, can someone explain how to solve? **Bus Departure Time Distribution**The time (in minutes) until the next bus departs a major bus depot follows a uniform distribution with $ f(x) = \frac{1}{20} $, where $ x $ ranges fr

The probability density function (PDF) of the uniformly distributed random variable with parameters…

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The time (in minutes) until the next bus departs a major bus depot follows a distribution with f(x) = where x goes from 25 to 45 minutes. O Part (a) O Part (b) O Part (e) O Part (d) O Part (e) O Part (0 O Part (g) O Part (h) Find the probability that the time is between 35 and 40 minutes. (Enter your answer as a fraction.) Sketch and label a graph of the distribution. Shade the area of interest. f(X) f(X) 0.20- 0.20 0.15 0.15 0.10 0.10 0.05 0.05 X 5 10 15 20 25 30 35 40 45 50 5 10 15 20 25 30 35 40 45 50 f(X) f(X) 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 5 10 15 20 25 30 35 40 45 50 5 10 15 20 25 30 35 40 45 50 Write the answer in a probability statement. (Enter exact numbers as integers, fractions, or decimals.) The probability of a waiting time --Select--v 35 minutes an v ---Select- ninutes is J. given waiting times - (? V less than

The time (in minutes) until the next bus departs a major bus depot follows a distribution with f(x) = where x goes from 25 to 45 minutes. O Part (a) O Part (b) O Part (e) O Part (d) O Part (e) O Part (0 O Part (g) O Part (h) Find the probability that the time is between 35 and 40 minutes. (Enter your answer as a fraction.) Sketch and label a graph of the distribution. Shade the area of interest. f(X) f(X) 0.20- 0.20 0.15 0.15 0.10 0.10 0.05 0.05 X 5 10 15 20 25 30 35 40 45 50 5 10 15 20 25 30 35 40 45 50 f(X) f(X) 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 5 10 15 20 25 30 35 40 45 50 5 10 15 20 25 30 35 40 45 50 Write the answer in a probability statement. (Enter exact numbers as integers, fractions, or decimals.) The probability of a waiting time --Select--v 35 minutes an v ---Select- ninutes is J. given waiting times - (? V less than

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Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.

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i keep getting these wrong, can someone explain how to solve?

**Bus Departure Time Distribution**

The time (in minutes) until the next bus departs a major bus depot follows a uniform distribution with $ f(x) = \frac{1}{20} $, where $ x $ ranges from 25 to 45 minutes.

**Problem:**
Find the probability that the time is between 35 and 40 minutes. (Enter your answer as a fraction.)

**Visual Explanation:**

Four histograms are provided to represent the uniform distribution:

1. **Histogram 1:**
- **Y-axis:** $ f(x) $ ranging from 0 to 0.20
- **X-axis:** Time from 0 to 50 minutes
- **Shaded Area:** Between 35 and 40 minutes
- **Description:** This plot highlights the uniform distribution where the area of interest is the shaded region between 35 and 40.

2. **Histogram 2:**
- Similar structure as Histogram 1
- Provides a visual focus on the shaded probability area between 35 and 40.

3. **Histogram 3:**
- Shows the full distribution curve with emphasis on the complete area of interest between 25 and 45 minutes.
- The same shaded region for probabilities between 35 and 40.

4. **Histogram 4:**
- Shows a cumulative probability distribution.
- Shaded area illustrates cumulative probabilities up to 40 minutes.

Upon solving, you will find the probability by calculating the area of the shaded region in proportion to the entire distribution.

**Probability Calculation:**

Write the answer as a probability statement, indicating the probability that a waiting time between 35 and 40 minutes occurs, given the specified uniform distribution.

**Educational Content:**

**Distribution Analysis for Bus Departure Times**

The time (in minutes) until the next bus departs a major bus depot follows a uniform distribution, given by the probability density function:

\[ f(x) = \frac{1}{20} \]

This function is valid for $x$ ranging from 25 to 45 minutes.

**Objective:**

Find the probability that the time is between 35 and 40 minutes.

**Solution Steps:**

1. **Calculate the Probability:**
- To find the probability that the bus departs between 35 and 40 minutes, integrate the probability density function $f(x)$ over this interval.

2. **Graphical Representation:**
- The graph of the uniform distribution is a horizontal line at $f(x) = 0.05$ from $x = 25$ to $x = 45$. The area of interest (35 to 40 minutes) is shaded on this graph.

3. **Graph Explanation:**
- **First Graph:** Displays the uniform distribution from 0 to 50 minutes, with a focus between 35 and 40 minutes.
- **Second Graph:** Highlights the same interval with markings to show the probability density function value.
- **Third Graph:** Demonstrates the uniform distribution again, indicating the continuous nature of the probability distribution.

**Probability Statement:**

- Use the graphical representation and integration to confirm the probability related to the range of interest.
- Complete the sentence: "The probability of a waiting time between 35 and 40 minutes is $\frac{1}{4}$, given waiting times from 25 to 45 minutes."

This overview helps in understanding the application of uniform distributions to real-world situations, such as predicting bus departure times.

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