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In a business, it is assumed that the average daily sales in (Rs.) follow normal
distribution. It is given that probability of average daily sales less than Rs. 124 is 0.0287
and the probability it exceeds Rs. 270 is 0.4599. Find parameters of this distribution.?
distribution. It is given that probability of average daily sales less than Rs. 124 is 0.0287
and the probability it exceeds Rs. 270 is 0.4599. Find parameters of this distribution.?
Most Upvoted Answer
In a business, it is assumed that the average daily sales in (Rs.) fol...
Solution:
Given, the probability of average daily sales less than Rs. 124 is 0.0287 and the probability it exceeds Rs. 270 is 0.4599.
Let the mean be μ and the standard deviation be σ.
1. Finding the Z-scores:
Using the standard normal distribution table, we can find the Z-scores for the given probabilities:
For P(X < 124),="" z="(124" -="" μ)="" σ="-1.88" />
For P(X > 270), Z = (270 - μ) / σ = 1.79
2. Finding the parameters:
Using the Z-scores and the properties of the standard normal distribution, we can find the values of μ and σ:
From Z = -1.88, we have P(Z < -1.88)="0.0287" />
Looking up in the standard normal distribution table, we get
P(Z < -1.88)="0.0301" />
Therefore, we can write:
(124 - μ) / σ = -1.88
Solving for μ, we get:
μ = 124 + 1.88σ
From Z = 1.79, we have P(Z > 1.79) = 0.4599
Looking up in the standard normal distribution table, we get
P(Z < 1.79)="0.9633" />
Therefore, we can write:
(270 - μ) / σ = 1.79
Substituting the value of μ, we get:
(270 - 124 - 1.88σ) / σ = 1.79
Solving for σ, we get:
σ ≈ 62.8
Substituting the value of σ in the equation for μ, we get:
μ ≈ 238.4
Therefore, the parameters of this distribution are:
Mean (μ) ≈ 238.4
Standard deviation (σ) ≈ 62.8
Conclusion:
Hence, we can conclude that the average daily sales in the business follow a normal distribution with mean (μ) ≈ 238.4 and standard deviation (σ) ≈ 62.8.
Given, the probability of average daily sales less than Rs. 124 is 0.0287 and the probability it exceeds Rs. 270 is 0.4599.
Let the mean be μ and the standard deviation be σ.
1. Finding the Z-scores:
Using the standard normal distribution table, we can find the Z-scores for the given probabilities:
For P(X < 124),="" z="(124" -="" μ)="" σ="-1.88" />
For P(X > 270), Z = (270 - μ) / σ = 1.79
2. Finding the parameters:
Using the Z-scores and the properties of the standard normal distribution, we can find the values of μ and σ:
From Z = -1.88, we have P(Z < -1.88)="0.0287" />
Looking up in the standard normal distribution table, we get
P(Z < -1.88)="0.0301" />
Therefore, we can write:
(124 - μ) / σ = -1.88
Solving for μ, we get:
μ = 124 + 1.88σ
From Z = 1.79, we have P(Z > 1.79) = 0.4599
Looking up in the standard normal distribution table, we get
P(Z < 1.79)="0.9633" />
Therefore, we can write:
(270 - μ) / σ = 1.79
Substituting the value of μ, we get:
(270 - 124 - 1.88σ) / σ = 1.79
Solving for σ, we get:
σ ≈ 62.8
Substituting the value of σ in the equation for μ, we get:
μ ≈ 238.4
Therefore, the parameters of this distribution are:
Mean (μ) ≈ 238.4
Standard deviation (σ) ≈ 62.8
Conclusion:
Hence, we can conclude that the average daily sales in the business follow a normal distribution with mean (μ) ≈ 238.4 and standard deviation (σ) ≈ 62.8.
Community Answer
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In a business, it is assumed that the average daily sales in (Rs.) follow normal distribution. It is given that probability of average daily sales less than Rs. 124 is 0.0287 and the probability it exceeds Rs. 270 is 0.4599. Find parameters of this distribution.?
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In a business, it is assumed that the average daily sales in (Rs.) follow normal distribution. It is given that probability of average daily sales less than Rs. 124 is 0.0287 and the probability it exceeds Rs. 270 is 0.4599. Find parameters of this distribution.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In a business, it is assumed that the average daily sales in (Rs.) follow normal distribution. It is given that probability of average daily sales less than Rs. 124 is 0.0287 and the probability it exceeds Rs. 270 is 0.4599. Find parameters of this distribution.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a business, it is assumed that the average daily sales in (Rs.) follow normal distribution. It is given that probability of average daily sales less than Rs. 124 is 0.0287 and the probability it exceeds Rs. 270 is 0.4599. Find parameters of this distribution.?.
In a business, it is assumed that the average daily sales in (Rs.) follow normal distribution. It is given that probability of average daily sales less than Rs. 124 is 0.0287 and the probability it exceeds Rs. 270 is 0.4599. Find parameters of this distribution.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In a business, it is assumed that the average daily sales in (Rs.) follow normal distribution. It is given that probability of average daily sales less than Rs. 124 is 0.0287 and the probability it exceeds Rs. 270 is 0.4599. Find parameters of this distribution.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a business, it is assumed that the average daily sales in (Rs.) follow normal distribution. It is given that probability of average daily sales less than Rs. 124 is 0.0287 and the probability it exceeds Rs. 270 is 0.4599. Find parameters of this distribution.?.
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