A population of values has a normal distribution with u = 95.4 and o = 45.4. A random sample of size n = 95 is drawn. a. Find the probability that a single randomly selected value is between 81 and 81.4. Round your answer to four decimal places. P(81 < X < 81.4) = b. Find the probability that a sample of size n = 95 is randomly selected with a mean between 81 and 81.4. Round your answer to four decimal places. P(81 < M < 81.4) : %3D
A population of values has a normal distribution with u = 95.4 and o = 45.4. A random sample of size n = 95 is drawn. a. Find the probability that a single randomly selected value is between 81 and 81.4. Round your answer to four decimal places. P(81 < X < 81.4) = b. Find the probability that a sample of size n = 95 is randomly selected with a mean between 81 and 81.4. Round your answer to four decimal places. P(81 < M < 81.4) : %3D
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
![## Probability and Statistics: Normal Distribution Problem
A population of values has a normal distribution with a mean (\(\mu\)) of 95.4 and a standard deviation (\(\sigma\)) of 45.4. A random sample of size \(n = 95\) is drawn.
### Problem Statement
#### a. Probability for a Single Randomly Selected Value
Find the probability that a single randomly selected value \(X\) lies between 81 and 81.4. Round your answer to four decimal places.
\[
P(81 < X < 81.4) = \, \underline{\phantom{answer}}
\]
#### b. Probability for a Sample Mean
Find the probability that a sample mean \(M\) for \(n = 95\) is randomly selected with a mean between 81 and 81.4. Round your answer to four decimal places.
\[
P(81 < M < 81.4) = \, \underline{\phantom{answer}}
\]
### Additional Information
- **Submit Question**: Once you have calculated the probabilities, you can submit your answers using the "Submit Question" button provided.
This exercise will help you understand how to use normal distributions to calculate probabilities for individual values and sample means within specified ranges. Make sure to use the properties of the normal distribution and possibly standard normal tables or calculators to find the required probabilities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7c3dd81-20a5-42d7-a935-4332a276b2b8%2F8826afb7-344b-446b-87b9-8849d7d2ea6c%2Fv9l2dlg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Probability and Statistics: Normal Distribution Problem
A population of values has a normal distribution with a mean (\(\mu\)) of 95.4 and a standard deviation (\(\sigma\)) of 45.4. A random sample of size \(n = 95\) is drawn.
### Problem Statement
#### a. Probability for a Single Randomly Selected Value
Find the probability that a single randomly selected value \(X\) lies between 81 and 81.4. Round your answer to four decimal places.
\[
P(81 < X < 81.4) = \, \underline{\phantom{answer}}
\]
#### b. Probability for a Sample Mean
Find the probability that a sample mean \(M\) for \(n = 95\) is randomly selected with a mean between 81 and 81.4. Round your answer to four decimal places.
\[
P(81 < M < 81.4) = \, \underline{\phantom{answer}}
\]
### Additional Information
- **Submit Question**: Once you have calculated the probabilities, you can submit your answers using the "Submit Question" button provided.
This exercise will help you understand how to use normal distributions to calculate probabilities for individual values and sample means within specified ranges. Make sure to use the properties of the normal distribution and possibly standard normal tables or calculators to find the required probabilities.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON

The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman

Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman