The number of seconds X after the minute that class ends is uniformly distributed between 0 and 60. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - U0 60 then the sampling distribution is b. Suppose that 40 classes are clocked. What is the distribution of a for this group of classes? - N( 30 2.7386 O Or c. What is the probability that the average of 40 classes will end with the second hand between 29 and 32 seconds? 0.1967 X Ⓡ Hint: Hint Textbook Pages Submit Question O O
The number of seconds X after the minute that class ends is uniformly distributed between 0 and 60. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - U0 60 then the sampling distribution is b. Suppose that 40 classes are clocked. What is the distribution of a for this group of classes? - N( 30 2.7386 O Or c. What is the probability that the average of 40 classes will end with the second hand between 29 and 32 seconds? 0.1967 X Ⓡ Hint: Hint Textbook Pages Submit Question O O
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Author:Amos Gilat
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![### Uniform Distribution of Time After the Minute - Educational Exercise
**Problem Statement:**
The number of seconds \( X \) after the minute that class ends is uniformly distributed between 0 and 60. Round all answers to 4 decimal places where possible.
**Solution:**
**a. What is the distribution of \( X \)?**
\( X \sim U(0, 60) \)
**b. Then the sampling distribution is:**
**Suppose that 40 classes are clocked. What is the distribution of \( \bar{X} \) for this group of classes?**
\( \bar{X} \sim N(30, 2.7386) \)
**c. What is the probability that the average of 40 classes will end with the second hand between 29 and 32 seconds?**
\( \text{Probability} = 0.1967 \) *(Note: this answer was marked incorrect in the exercise.)*
**Hint:**
[Hint link]
**Textbook Pages:**
[Textbook link]
**Submission:**
Click "Submit Question" when you are ready to submit your answers for evaluation.
---
### Explanation of Concepts:
**Uniform Distribution:**
A uniform distribution is a type of probability distribution in which all outcomes are equally likely. If \( X \) is uniformly distributed between \( a \) and \( b \), it is denoted as \( X \sim U(a, b) \).
**Sampling Distribution:**
The sampling distribution of the sample mean \( \bar{X} \) from a population with mean \( \mu \) and variance \( \sigma^2 \) with a sample size \( n \) is normally distributed when the sample size is large (Central Limit Theorem). The distribution is denoted as \( \bar{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}}) \).
**Probability Calculation:**
The probability that the average of 40 classes will end with the second hand between 29 and 32 seconds involves calculating the area under the normal distribution curve between these two points. This requires the use of z-scores and standard normal distribution tables or computational tools.
**Visualization:**
The image provided does not contain visual diagrams or graphs, but it primarily includes text-based math problems and their corresponding answers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba867a91-7946-4dc8-8b92-57b0d80fa10e%2F6ce73b4b-f14f-45dc-98bd-33a3ac79bd87%2F3qd3th_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Uniform Distribution of Time After the Minute - Educational Exercise
**Problem Statement:**
The number of seconds \( X \) after the minute that class ends is uniformly distributed between 0 and 60. Round all answers to 4 decimal places where possible.
**Solution:**
**a. What is the distribution of \( X \)?**
\( X \sim U(0, 60) \)
**b. Then the sampling distribution is:**
**Suppose that 40 classes are clocked. What is the distribution of \( \bar{X} \) for this group of classes?**
\( \bar{X} \sim N(30, 2.7386) \)
**c. What is the probability that the average of 40 classes will end with the second hand between 29 and 32 seconds?**
\( \text{Probability} = 0.1967 \) *(Note: this answer was marked incorrect in the exercise.)*
**Hint:**
[Hint link]
**Textbook Pages:**
[Textbook link]
**Submission:**
Click "Submit Question" when you are ready to submit your answers for evaluation.
---
### Explanation of Concepts:
**Uniform Distribution:**
A uniform distribution is a type of probability distribution in which all outcomes are equally likely. If \( X \) is uniformly distributed between \( a \) and \( b \), it is denoted as \( X \sim U(a, b) \).
**Sampling Distribution:**
The sampling distribution of the sample mean \( \bar{X} \) from a population with mean \( \mu \) and variance \( \sigma^2 \) with a sample size \( n \) is normally distributed when the sample size is large (Central Limit Theorem). The distribution is denoted as \( \bar{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}}) \).
**Probability Calculation:**
The probability that the average of 40 classes will end with the second hand between 29 and 32 seconds involves calculating the area under the normal distribution curve between these two points. This requires the use of z-scores and standard normal distribution tables or computational tools.
**Visualization:**
The image provided does not contain visual diagrams or graphs, but it primarily includes text-based math problems and their corresponding answers.
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