Question 1192345: Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is σ= 9 milligrams. Juan repeats the measurement 3 times and records the mean x of his 3 measurements.
A) What is the standard deviation (±0.01) of Juan's mean result? (That is, if Juan kept on making 3 measurements and averaging them, what would be the standard deviation of all his x's?)
B) How many times must Juan repeat the measurement so that the standard deviation of x is 2? (Round your answer to the nearest whole number.)
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! **A) Standard Deviation of Juan's Mean Result**
* **Concept:** The standard deviation of the sample mean (x̄) is also known as the **standard error of the mean**.
* **Formula:** Standard Error (SE) = σ / √n
* where σ is the population standard deviation and n is the sample size.
* **Given:** σ = 9 milligrams, n = 3 measurements
* **Calculation:** SE = 9 / √3 ≈ 5.196 milligrams
* **Standard Deviation of Juan's Mean Result:** 5.20 milligrams (rounded to 2 decimal places)
**B) Number of Measurements for Standard Deviation of x = 2**
* **Rearrange the Standard Error formula:**
* SE = σ / √n
* √n = σ / SE
* n = (σ / SE)²
* **Given:** σ = 9 milligrams, SE = 2 milligrams
* **Calculation:** n = (9 / 2)² = 20.25
* **Number of Measurements:** 21 (rounded to the nearest whole number)
**In summary:**
* A) The standard deviation of Juan's mean result is 5.20 milligrams.
* B) Juan must repeat the measurement 21 times to achieve a standard deviation of his mean result of 2 milligrams.
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