Commerce Exam > Commerce Questions > In a normal distribution 31 per cent of the i...
Start Learning for Free
In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.?
Most Upvoted Answer
In a normal distribution 31 per cent of the items are under 45 and 8 p...
Understanding the Problem
In a normal distribution, we know that the mean (μ) and standard deviation (σ) can be determined using the provided percentiles. We have:
- 31% of items are under 45
- 8% of items are over 64
Step 1: Identify Z-scores
Using standard normal distribution tables:
- For 31% below 45, the Z-score is approximately -0.50.
- For 92% (100% - 8%) below 64, the Z-score is approximately 1.41.
Step 2: Set Up Equations
Using the Z-score formula:
- Z = (X - μ) / σ
We can set up two equations based on the Z-scores:
Step 3: Solve the Equations
From the first equation, we can express μ in terms of σ:
Substituting this into the second equation:
This simplifies to:
Step 4: Calculate Mean (μ)
Now plug σ back into the equation for μ:
Final Results
- Mean (μ) ≈ 49.48
- Standard Deviation (σ) ≈ 9.95
These calculations give the mean and standard deviation of the normal distribution based on the provided percentiles.
In a normal distribution, we know that the mean (μ) and standard deviation (σ) can be determined using the provided percentiles. We have:
- 31% of items are under 45
- 8% of items are over 64
Step 1: Identify Z-scores
Using standard normal distribution tables:
- For 31% below 45, the Z-score is approximately -0.50.
- For 92% (100% - 8%) below 64, the Z-score is approximately 1.41.
Step 2: Set Up Equations
Using the Z-score formula:
- Z = (X - μ) / σ
We can set up two equations based on the Z-scores:
- For 45: -0.50 = (45 - μ) / σ
- For 64: 1.41 = (64 - μ) / σ
Step 3: Solve the Equations
From the first equation, we can express μ in terms of σ:
- μ = 45 + 0.50σ
Substituting this into the second equation:
- 1.41 = (64 - (45 + 0.50σ)) / σ
This simplifies to:
- 1.41σ = 19 - 0.50σ
- 1.91σ = 19
- σ ≈ 9.95
Step 4: Calculate Mean (μ)
Now plug σ back into the equation for μ:
- μ = 45 + 0.50 * 9.95 ≈ 49.48
Final Results
- Mean (μ) ≈ 49.48
- Standard Deviation (σ) ≈ 9.95
These calculations give the mean and standard deviation of the normal distribution based on the provided percentiles.
Attention Commerce Students!
To make sure you are not studying endlessly, EduRev has designed Commerce study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Commerce.
|
Explore Courses for Commerce exam
|
|
Top Courses for CommerceView all
In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.?
Question Description
In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.? for Commerce 2024 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.? covers all topics & solutions for Commerce 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.?.
In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.? for Commerce 2024 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.? covers all topics & solutions for Commerce 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.?.
Solutions for In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.? in English & in Hindi are available as part of our courses for Commerce.
Download more important topics, notes, lectures and mock test series for Commerce Exam by signing up for free.
Here you can find the meaning of In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.? defined & explained in the simplest way possible. Besides giving the explanation of
In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.?, a detailed solution for In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.? has been provided alongside types of In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.? theory, EduRev gives you an
ample number of questions to practice In a normal distribution 31 per cent of the items are under 45 and 8 per cent are over 64. Find the mean and standard deviation of the distribution.? tests, examples and also practice Commerce tests.
|
|
Explore Courses for Commerce exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup