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The mean of monthly expenditure of a batch of students is100 with standard deviation is 20 if the expenditure is normally distribute find out the maximum expenditure of those 10% of students whose expenditure is lowest?
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The mean of monthly expenditure of a batch of students is100 with stan...
Maximum Expenditure of the Lowest 10% of Students
In order to find out the maximum expenditure of the lowest 10% of students, we need to calculate the corresponding z-score and then convert it back to the expenditure value.
Step 1: Find the z-score
- The mean monthly expenditure is given as 100.
- The standard deviation is given as 20.
- We need to find the z-score corresponding to the lowest 10% of students.
Step 2: Find the z-score from the standard normal distribution table
- The standard normal distribution table provides z-scores corresponding to different percentiles.
- Since we are looking for the lowest 10%, we need to find the z-score for the 10th percentile.
- The 10th percentile corresponds to a cumulative probability of 0.10.
Looking at the standard normal distribution table, we find that the z-score corresponding to a cumulative probability of 0.10 is approximately -1.28.
Step 3: Convert the z-score back to the expenditure value
- We have the z-score of -1.28.
- We can use the formula z = (x - μ) / σ, where x is the expenditure value, μ is the mean, and σ is the standard deviation.
- Rearranging the formula, we get x = z * σ + μ.
Substituting the values, we get x = -1.28 * 20 + 100 = 74.4.
Therefore, the maximum expenditure of the lowest 10% of students is approximately 74.4.
Conclusion
The maximum expenditure of the lowest 10% of students is found to be approximately 74.4. This means that 10% of the students have an expenditure lower than or equal to 74.4.
In order to find out the maximum expenditure of the lowest 10% of students, we need to calculate the corresponding z-score and then convert it back to the expenditure value.
Step 1: Find the z-score
- The mean monthly expenditure is given as 100.
- The standard deviation is given as 20.
- We need to find the z-score corresponding to the lowest 10% of students.
Step 2: Find the z-score from the standard normal distribution table
- The standard normal distribution table provides z-scores corresponding to different percentiles.
- Since we are looking for the lowest 10%, we need to find the z-score for the 10th percentile.
- The 10th percentile corresponds to a cumulative probability of 0.10.
Looking at the standard normal distribution table, we find that the z-score corresponding to a cumulative probability of 0.10 is approximately -1.28.
Step 3: Convert the z-score back to the expenditure value
- We have the z-score of -1.28.
- We can use the formula z = (x - μ) / σ, where x is the expenditure value, μ is the mean, and σ is the standard deviation.
- Rearranging the formula, we get x = z * σ + μ.
Substituting the values, we get x = -1.28 * 20 + 100 = 74.4.
Therefore, the maximum expenditure of the lowest 10% of students is approximately 74.4.
Conclusion
The maximum expenditure of the lowest 10% of students is found to be approximately 74.4. This means that 10% of the students have an expenditure lower than or equal to 74.4.
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The mean of monthly expenditure of a batch of students is100 with standard deviation is 20 if the expenditure is normally distribute find out the maximum expenditure of those 10% of students whose expenditure is lowest?
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The mean of monthly expenditure of a batch of students is100 with standard deviation is 20 if the expenditure is normally distribute find out the maximum expenditure of those 10% of students whose expenditure is lowest? 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 The mean of monthly expenditure of a batch of students is100 with standard deviation is 20 if the expenditure is normally distribute find out the maximum expenditure of those 10% of students whose expenditure is lowest? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean of monthly expenditure of a batch of students is100 with standard deviation is 20 if the expenditure is normally distribute find out the maximum expenditure of those 10% of students whose expenditure is lowest?.
The mean of monthly expenditure of a batch of students is100 with standard deviation is 20 if the expenditure is normally distribute find out the maximum expenditure of those 10% of students whose expenditure is lowest? 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 The mean of monthly expenditure of a batch of students is100 with standard deviation is 20 if the expenditure is normally distribute find out the maximum expenditure of those 10% of students whose expenditure is lowest? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean of monthly expenditure of a batch of students is100 with standard deviation is 20 if the expenditure is normally distribute find out the maximum expenditure of those 10% of students whose expenditure is lowest?.
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