a. What is the distribution of X? X - N( b. What is the distribution of ? - N c. What is the distribution of ? - N d. If one randomly selected student is timed find th T.
a. What is the distribution of X? X - N( b. What is the distribution of ? - N c. What is the distribution of ? - N d. If one randomly selected student is timed find th T.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![**Study Time Distribution Analysis**
Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with a mean of 41 minutes and a standard deviation of 22 minutes. A researcher observed 17 students who entered the library to study. Round all answers to 4 decimal places where possible.
**a. Distribution of Individual Study Time**
What is the distribution of \( X? \; X \sim N( \_\_\_\_\_\_\_ , \_\_\_\_\_\_\_ ) \)
**b. Distribution of Sample Mean**
What is the distribution of \( \overline{X} ? \; \overline{X} \sim N( \_\_\_\_\_\_\_ , \_\_\_\_\_\_\_ ) \)
**c. Distribution of Total Study Time**
What is the distribution of \( \sum x? \; \sum x \sim N( \_\_\_\_\_\_\_ , \_\_\_\_\_\_\_ ) \)
**d. Probability for a Specific Range of Individual Study Time**
If one randomly selected student is timed, find the probability that this student's time will be between 34 and 38 minutes.
\[ \text{Probability} = \_\_\_\_ \]
**e. Probability for the Average Study Time of 17 Students**
For the 17 students, find the probability that their average time studying is between 34 and 38 minutes.
\[ \text{Probability} = \_\_\_\_ \]
**f. Total Study Time Exceeding a Certain Value**
Find the probability that the randomly selected 17 students will have a total study time of more than 765 minutes.
\[ \text{Probability} = \_\_\_\_ \]
**g. Assumption of Normal Distribution**
For part e) and f), is the assumption of normality necessary?
\[ \text{Answer} = \boxed{\text{Yes}} \hspace{5pt} \boxed{\text{No}} \]
**h. Lowest Total Study Time for Recognition**
The top 10% of the total study time for groups of 17 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker?
\[ \text{Least Total Time} = \_\_\_\_ \text{minutes} \]
**Hint:**
Some Helpful Videos](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53c2050e-df40-4c0a-8720-81a391ef4121%2F48994a90-ee6e-41ae-929c-68cb1c238266%2Fyth4uw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Study Time Distribution Analysis**
Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with a mean of 41 minutes and a standard deviation of 22 minutes. A researcher observed 17 students who entered the library to study. Round all answers to 4 decimal places where possible.
**a. Distribution of Individual Study Time**
What is the distribution of \( X? \; X \sim N( \_\_\_\_\_\_\_ , \_\_\_\_\_\_\_ ) \)
**b. Distribution of Sample Mean**
What is the distribution of \( \overline{X} ? \; \overline{X} \sim N( \_\_\_\_\_\_\_ , \_\_\_\_\_\_\_ ) \)
**c. Distribution of Total Study Time**
What is the distribution of \( \sum x? \; \sum x \sim N( \_\_\_\_\_\_\_ , \_\_\_\_\_\_\_ ) \)
**d. Probability for a Specific Range of Individual Study Time**
If one randomly selected student is timed, find the probability that this student's time will be between 34 and 38 minutes.
\[ \text{Probability} = \_\_\_\_ \]
**e. Probability for the Average Study Time of 17 Students**
For the 17 students, find the probability that their average time studying is between 34 and 38 minutes.
\[ \text{Probability} = \_\_\_\_ \]
**f. Total Study Time Exceeding a Certain Value**
Find the probability that the randomly selected 17 students will have a total study time of more than 765 minutes.
\[ \text{Probability} = \_\_\_\_ \]
**g. Assumption of Normal Distribution**
For part e) and f), is the assumption of normality necessary?
\[ \text{Answer} = \boxed{\text{Yes}} \hspace{5pt} \boxed{\text{No}} \]
**h. Lowest Total Study Time for Recognition**
The top 10% of the total study time for groups of 17 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker?
\[ \text{Least Total Time} = \_\_\_\_ \text{minutes} \]
**Hint:**
Some Helpful Videos
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