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In a business it is assumed that the average daily sales expressed in Rupees following normal distribution.Find the coefficient of variation of sales given that the probability that the average daily sales is less than Rs. 124 is 0.0287 and the probability that the average daily sales is more than Rs. 270 is 0.4599. Ans: Mean =2627 5D=73 CV =26.79 Ans: Mean =2627 5D=73?
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In a business it is assumed that the average daily sales expressed in ...
Given data:
- The average daily sales follow normal distribution
- The probability that the average daily sales is less than Rs. 124 is 0.0287
- The probability that the average daily sales is more than Rs. 270 is 0.4599
To find:
- Coefficient of variation of sales
Solution:
1. Finding the mean:
Using the normal distribution table, we can find the z-score for each probability.
- For P(X < 124),="" z-score="" />
- For P(X > 270), z-score = 1.79
Now, we can use the formula:
z = (X - μ) / σ
where
z = z-score
X = sales value
μ = mean of sales
σ = standard deviation
Using the z-score values, we can write two equations:
- -1.88 = (124 - μ) / σ
- 1.79 = (270 - μ) / σ
Solving these equations simultaneously, we get:
μ = 2627.5
Therefore, the mean of sales is Rs. 2627.5.
2. Finding the 5D:
From the normal distribution table, we can find the z-score for P(X < μ="" -="" 2.5σ)="" and="" p(x="" /> μ + 2.5σ).
- For P(X < μ="" -="" 2.5σ),="" z-score="" />
- For P(X > μ + 2.5σ), z-score = 2.5
Using the formula z = (X - μ) / σ, we get two equations:
- -2.5 = (X - μ) / σ
- 2.5 = (X - μ) / σ
Solving for σ, we get:
σ = (X - μ) / 2.5
Now, we use the given probabilities to find the values of X:
- P(X < 124)="" />
Using the normal distribution table, we get the z-score = -1.88.
Substituting in the equation, we get:
124 - 2627.5 / σ = -1.88
Solving for σ, we get σ = 695.3
Therefore, 5D = 695.3 * 2.5 = 1738.25
- P(X > 270) = 0.4599
Using the normal distribution table, we get the z-score = 1.79.
Substituting in the equation, we get:
270 - 2627.5 / σ = 1.79
Solving for σ, we get σ = 650.9
Therefore, 5D = 650.9 * 2.5 = 1627.25
3. Finding the coefficient of variation:
Coefficient of variation (CV) is given by the formula:
CV = (σ / μ) * 100
Substituting the values, we get:
CV = (650.9 / 2627.5) * 100 = 24.77%
Therefore, the coefficient of variation of sales is 24.77%.
- The average daily sales follow normal distribution
- The probability that the average daily sales is less than Rs. 124 is 0.0287
- The probability that the average daily sales is more than Rs. 270 is 0.4599
To find:
- Coefficient of variation of sales
Solution:
1. Finding the mean:
Using the normal distribution table, we can find the z-score for each probability.
- For P(X < 124),="" z-score="" />
- For P(X > 270), z-score = 1.79
Now, we can use the formula:
z = (X - μ) / σ
where
z = z-score
X = sales value
μ = mean of sales
σ = standard deviation
Using the z-score values, we can write two equations:
- -1.88 = (124 - μ) / σ
- 1.79 = (270 - μ) / σ
Solving these equations simultaneously, we get:
μ = 2627.5
Therefore, the mean of sales is Rs. 2627.5.
2. Finding the 5D:
From the normal distribution table, we can find the z-score for P(X < μ="" -="" 2.5σ)="" and="" p(x="" /> μ + 2.5σ).
- For P(X < μ="" -="" 2.5σ),="" z-score="" />
- For P(X > μ + 2.5σ), z-score = 2.5
Using the formula z = (X - μ) / σ, we get two equations:
- -2.5 = (X - μ) / σ
- 2.5 = (X - μ) / σ
Solving for σ, we get:
σ = (X - μ) / 2.5
Now, we use the given probabilities to find the values of X:
- P(X < 124)="" />
Using the normal distribution table, we get the z-score = -1.88.
Substituting in the equation, we get:
124 - 2627.5 / σ = -1.88
Solving for σ, we get σ = 695.3
Therefore, 5D = 695.3 * 2.5 = 1738.25
- P(X > 270) = 0.4599
Using the normal distribution table, we get the z-score = 1.79.
Substituting in the equation, we get:
270 - 2627.5 / σ = 1.79
Solving for σ, we get σ = 650.9
Therefore, 5D = 650.9 * 2.5 = 1627.25
3. Finding the coefficient of variation:
Coefficient of variation (CV) is given by the formula:
CV = (σ / μ) * 100
Substituting the values, we get:
CV = (650.9 / 2627.5) * 100 = 24.77%
Therefore, the coefficient of variation of sales is 24.77%.
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In a business it is assumed that the average daily sales expressed in Rupees following normal distribution.Find the coefficient of variation of sales given that the probability that the average daily sales is less than Rs. 124 is 0.0287 and the probability that the average daily sales is more than Rs. 270 is 0.4599. Ans: Mean =2627 5D=73 CV =26.79 Ans: Mean =2627 5D=73?
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In a business it is assumed that the average daily sales expressed in Rupees following normal distribution.Find the coefficient of variation of sales given that the probability that the average daily sales is less than Rs. 124 is 0.0287 and the probability that the average daily sales is more than Rs. 270 is 0.4599. Ans: Mean =2627 5D=73 CV =26.79 Ans: Mean =2627 5D=73? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In a business it is assumed that the average daily sales expressed in Rupees following normal distribution.Find the coefficient of variation of sales given that the probability that the average daily sales is less than Rs. 124 is 0.0287 and the probability that the average daily sales is more than Rs. 270 is 0.4599. Ans: Mean =2627 5D=73 CV =26.79 Ans: Mean =2627 5D=73? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a business it is assumed that the average daily sales expressed in Rupees following normal distribution.Find the coefficient of variation of sales given that the probability that the average daily sales is less than Rs. 124 is 0.0287 and the probability that the average daily sales is more than Rs. 270 is 0.4599. Ans: Mean =2627 5D=73 CV =26.79 Ans: Mean =2627 5D=73?.
In a business it is assumed that the average daily sales expressed in Rupees following normal distribution.Find the coefficient of variation of sales given that the probability that the average daily sales is less than Rs. 124 is 0.0287 and the probability that the average daily sales is more than Rs. 270 is 0.4599. Ans: Mean =2627 5D=73 CV =26.79 Ans: Mean =2627 5D=73? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In a business it is assumed that the average daily sales expressed in Rupees following normal distribution.Find the coefficient of variation of sales given that the probability that the average daily sales is less than Rs. 124 is 0.0287 and the probability that the average daily sales is more than Rs. 270 is 0.4599. Ans: Mean =2627 5D=73 CV =26.79 Ans: Mean =2627 5D=73? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a business it is assumed that the average daily sales expressed in Rupees following normal distribution.Find the coefficient of variation of sales given that the probability that the average daily sales is less than Rs. 124 is 0.0287 and the probability that the average daily sales is more than Rs. 270 is 0.4599. Ans: Mean =2627 5D=73 CV =26.79 Ans: Mean =2627 5D=73?.
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In a business it is assumed that the average daily sales expressed in Rupees following normal distribution.Find the coefficient of variation of sales given that the probability that the average daily sales is less than Rs. 124 is 0.0287 and the probability that the average daily sales is more than Rs. 270 is 0.4599. Ans: Mean =2627 5D=73 CV =26.79 Ans: Mean =2627 5D=73?, a detailed solution for In a business it is assumed that the average daily sales expressed in Rupees following normal distribution.Find the coefficient of variation of sales given that the probability that the average daily sales is less than Rs. 124 is 0.0287 and the probability that the average daily sales is more than Rs. 270 is 0.4599. Ans: Mean =2627 5D=73 CV =26.79 Ans: Mean =2627 5D=73? has been provided alongside types of In a business it is assumed that the average daily sales expressed in Rupees following normal distribution.Find the coefficient of variation of sales given that the probability that the average daily sales is less than Rs. 124 is 0.0287 and the probability that the average daily sales is more than Rs. 270 is 0.4599. Ans: Mean =2627 5D=73 CV =26.79 Ans: Mean =2627 5D=73? theory, EduRev gives you an
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