UPSC Exam > UPSC Questions > The speed of number of bikes follow a Norma d...
Start Learning for Free
The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.?
Most Upvoted Answer
The speed of number of bikes follow a Norma distribution with a mean o...
To find the probability that a randomly picked bike is traveling between 83 km/hr and 95 km/hr, we will utilize the properties of the normal distribution.
Understanding the Normal Distribution
- The speed of bikes follows a normal distribution characterized by:
- Mean (μ) = 83 km/hr
- Standard Deviation (σ) = 9.4 km/hr
Standardizing the Values
- To calculate the probability, we first standardize the values using the Z-score formula:
- Z = (X - μ) / σ
- For 83 km/hr:
- Z1 = (83 - 83) / 9.4 = 0
- For 95 km/hr:
- Z2 = (95 - 83) / 9.4 ≈ 1.28
Finding the Probabilities
- Next, we look up the Z-scores in the standard normal distribution table:
- P(Z ≤ 0) = 0.5000 (for Z1 = 0)
- P(Z ≤ 1.28) ≈ 0.8997 (for Z2 ≈ 1.28)
Calculating the Desired Probability
- The probability that a bike is traveling between 83 km/hr and 95 km/hr is given by:
- P(83 ≤ X ≤ 95) = P(Z ≤ 1.28) - P(Z ≤ 0)
- P(83 ≤ X ≤ 95) ≈ 0.8997 - 0.5000 = 0.3997
Conclusion
- Therefore, the probability that a randomly selected bike is traveling between 83 km/hr and 95 km/hr is approximately 0.3997, or 39.97%. This indicates a significant likelihood that the bike's speed falls within this range.
Understanding the Normal Distribution
- The speed of bikes follows a normal distribution characterized by:
- Mean (μ) = 83 km/hr
- Standard Deviation (σ) = 9.4 km/hr
Standardizing the Values
- To calculate the probability, we first standardize the values using the Z-score formula:
- Z = (X - μ) / σ
- For 83 km/hr:
- Z1 = (83 - 83) / 9.4 = 0
- For 95 km/hr:
- Z2 = (95 - 83) / 9.4 ≈ 1.28
Finding the Probabilities
- Next, we look up the Z-scores in the standard normal distribution table:
- P(Z ≤ 0) = 0.5000 (for Z1 = 0)
- P(Z ≤ 1.28) ≈ 0.8997 (for Z2 ≈ 1.28)
Calculating the Desired Probability
- The probability that a bike is traveling between 83 km/hr and 95 km/hr is given by:
- P(83 ≤ X ≤ 95) = P(Z ≤ 1.28) - P(Z ≤ 0)
- P(83 ≤ X ≤ 95) ≈ 0.8997 - 0.5000 = 0.3997
Conclusion
- Therefore, the probability that a randomly selected bike is traveling between 83 km/hr and 95 km/hr is approximately 0.3997, or 39.97%. This indicates a significant likelihood that the bike's speed falls within this range.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.?
Question Description
The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.?.
The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.?.
Solutions for The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.? defined & explained in the simplest way possible. Besides giving the explanation of
The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.?, a detailed solution for The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.? has been provided alongside types of The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.? theory, EduRev gives you an
ample number of questions to practice The speed of number of bikes follow a Norma distribution with a mean of 83 km/hr. and a standard deviation of 9.4 km/hr. find the probability that a bike picked at random is travelling at 83 km/hr. to 95 km/hr.? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup