Suppose student Ana is running for a charity and asks her friend to chip in the donation. Suppose each friend donates independently, and the donated value T is a random variable with the following probability density: c ti € [5, 10] dollars с t € [35, 40] dollars. otherwise 0 Let's assume Te's are mutually independent and each donation is a continuous random variable given they're using electronic transfer. Ana requested from 150 friends for the Lot bo looted from thooo 150 friendo You p(Ti = ts) : = in de
Suppose student Ana is running for a charity and asks her friend to chip in the donation. Suppose each friend donates independently, and the donated value T is a random variable with the following probability density: c ti € [5, 10] dollars с t € [35, 40] dollars. otherwise 0 Let's assume Te's are mutually independent and each donation is a continuous random variable given they're using electronic transfer. Ana requested from 150 friends for the Lot bo looted from thooo 150 friendo You p(Ti = ts) : = in de
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Statistics CS
![Suppose student Ana is running for a charity and asks her friend to chip in the donation. Suppose each friend donates independently, and the donated value \( T_i \) is a random variable with the following probability density:
\[
p(T_i = t_i) =
\begin{cases}
c & t_i \in [5, 10] \text{ dollars} \\
c & t_i \in [35, 40] \text{ dollars} \\
0 & \text{otherwise}
\end{cases}
\]
Let's assume \( T_i \)'s are mutually independent and each donation is a continuous random variable given they're using electronic transfer. Ana requested from 150 friends for the donation. Let \( X \) be the total amount in dollars Ana collected from these 150 friends. You need to simplify for this problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1784d6b6-d0da-4ca6-88bb-f1a2aff3fb92%2F8df9b068-0755-4e4b-8cf2-b10f3cff564c%2Frwo9s_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose student Ana is running for a charity and asks her friend to chip in the donation. Suppose each friend donates independently, and the donated value \( T_i \) is a random variable with the following probability density:
\[
p(T_i = t_i) =
\begin{cases}
c & t_i \in [5, 10] \text{ dollars} \\
c & t_i \in [35, 40] \text{ dollars} \\
0 & \text{otherwise}
\end{cases}
\]
Let's assume \( T_i \)'s are mutually independent and each donation is a continuous random variable given they're using electronic transfer. Ana requested from 150 friends for the donation. Let \( X \) be the total amount in dollars Ana collected from these 150 friends. You need to simplify for this problem.
![For the remaining subquestions, assume \( T_i \) follows a normal distribution instead with a **mean of 10** and **variance of 28**.
**Question:**
What is the probability that \( X \) is more than 1519? Assume \( X \) is a normal distributed random variable. Use the given CDF table to solve.
\[
P(X > 1519) = \text{number (2 significant figures)}
\]
**Instructions:**
Which row and column (assuming 1-indexed, the title row, title column, and empty rows do not count) and round down/truncate in the given CDF table can be used to calculate the probability above? For example, for rounding if you get a z-score of 0.519, you should round up to .52, and if you get .514, you should round down to 0.51.
- **Row**: integer
- **Column**: integer
**Explanation:**
This question involves statistical concepts related to the normal distribution, where you need to use a CDF (Cumulative Distribution Function) table to find probabilities. You need to determine the z-score for 1519 using the mean and variance given, then reference the correct row and column in the CDF table for your calculations. This task requires rounding the z-score correctly based on given rules to ensure accuracy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1784d6b6-d0da-4ca6-88bb-f1a2aff3fb92%2F8df9b068-0755-4e4b-8cf2-b10f3cff564c%2F368wmvx_processed.png&w=3840&q=75)
Transcribed Image Text:For the remaining subquestions, assume \( T_i \) follows a normal distribution instead with a **mean of 10** and **variance of 28**.
**Question:**
What is the probability that \( X \) is more than 1519? Assume \( X \) is a normal distributed random variable. Use the given CDF table to solve.
\[
P(X > 1519) = \text{number (2 significant figures)}
\]
**Instructions:**
Which row and column (assuming 1-indexed, the title row, title column, and empty rows do not count) and round down/truncate in the given CDF table can be used to calculate the probability above? For example, for rounding if you get a z-score of 0.519, you should round up to .52, and if you get .514, you should round down to 0.51.
- **Row**: integer
- **Column**: integer
**Explanation:**
This question involves statistical concepts related to the normal distribution, where you need to use a CDF (Cumulative Distribution Function) table to find probabilities. You need to determine the z-score for 1519 using the mean and variance given, then reference the correct row and column in the CDF table for your calculations. This task requires rounding the z-score correctly based on given rules to ensure accuracy.
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