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In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectively
- a)90 and 9
- b)9 and 90
- c)0.9 and 90
- d)90 and 0.9
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
In a manufacturing plant, the probability of making a defective bolt i...
It’s a poission distribution. Here n = 900, p = 0.1
∴ mean (m)= np = 900 × 0.1 = 90
Standard deviat ion (σ)=
= √81 = 9 (∵ σ > 0).,
∴ mean (m)= np = 900 × 0.1 = 90
Standard deviat ion (σ)=
= √81 = 9 (∵ σ > 0).,
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In a manufacturing plant, the probability of making a defective bolt i...
Problem:
In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectively
a) 90 and 9
b) 9 and 90
c) 0.9 and 90
d) 90 and 0.9
Solution:
To solve this problem, we need to understand the relationship between probability, mean, and standard deviation.
Mean:
The mean is the average value of a set of numbers. In this case, the mean represents the expected number of defective bolts out of the total 900 bolts.
Standard Deviation:
The standard deviation measures the amount of variation or dispersion in a set of numbers. In this case, the standard deviation represents the spread or variability in the number of defective bolts.
Probability:
The probability of making a defective bolt is given as 0.1, which means that out of every 10 bolts produced, one bolt is expected to be defective.
Calculating the Mean:
To calculate the mean, we multiply the total number of bolts by the probability of making a defective bolt.
Mean = Total Number of Bolts * Probability
Mean = 900 * 0.1
Mean = 90
Hence, the mean of defective bolts in a total of 900 bolts is 90.
Calculating the Standard Deviation:
To calculate the standard deviation, we use the formula:
Standard Deviation = Square Root of (Total Number of Bolts × Probability × (1 - Probability))
Standard Deviation = √(900 × 0.1 × (1 - 0.1))
Standard Deviation = √(900 × 0.1 × 0.9)
Standard Deviation = √(81)
Standard Deviation = 9
Hence, the standard deviation of defective bolts in a total of 900 bolts is 9.
Conclusion:
The mean and standard deviation of defective bolts in a total of 900 bolts are 90 and 9, respectively. Therefore, the correct answer is option A) 90 and 9.
In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectively
a) 90 and 9
b) 9 and 90
c) 0.9 and 90
d) 90 and 0.9
Solution:
To solve this problem, we need to understand the relationship between probability, mean, and standard deviation.
Mean:
The mean is the average value of a set of numbers. In this case, the mean represents the expected number of defective bolts out of the total 900 bolts.
Standard Deviation:
The standard deviation measures the amount of variation or dispersion in a set of numbers. In this case, the standard deviation represents the spread or variability in the number of defective bolts.
Probability:
The probability of making a defective bolt is given as 0.1, which means that out of every 10 bolts produced, one bolt is expected to be defective.
Calculating the Mean:
To calculate the mean, we multiply the total number of bolts by the probability of making a defective bolt.
Mean = Total Number of Bolts * Probability
Mean = 900 * 0.1
Mean = 90
Hence, the mean of defective bolts in a total of 900 bolts is 90.
Calculating the Standard Deviation:
To calculate the standard deviation, we use the formula:
Standard Deviation = Square Root of (Total Number of Bolts × Probability × (1 - Probability))
Standard Deviation = √(900 × 0.1 × (1 - 0.1))
Standard Deviation = √(900 × 0.1 × 0.9)
Standard Deviation = √(81)
Standard Deviation = 9
Hence, the standard deviation of defective bolts in a total of 900 bolts is 9.
Conclusion:
The mean and standard deviation of defective bolts in a total of 900 bolts are 90 and 9, respectively. Therefore, the correct answer is option A) 90 and 9.
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In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectivelya)90 and 9b)9 and 90c)0.9and 90d)90 and 0.9Correct answer is option 'A'. Can you explain this answer?
Question Description
In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectivelya)90 and 9b)9 and 90c)0.9and 90d)90 and 0.9Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectivelya)90 and 9b)9 and 90c)0.9and 90d)90 and 0.9Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectivelya)90 and 9b)9 and 90c)0.9and 90d)90 and 0.9Correct answer is option 'A'. Can you explain this answer?.
In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectivelya)90 and 9b)9 and 90c)0.9and 90d)90 and 0.9Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectivelya)90 and 9b)9 and 90c)0.9and 90d)90 and 0.9Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectivelya)90 and 9b)9 and 90c)0.9and 90d)90 and 0.9Correct answer is option 'A'. Can you explain this answer?.
Solutions for In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectivelya)90 and 9b)9 and 90c)0.9and 90d)90 and 0.9Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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