Calculating Standard Deviation for a Sample of Batteries

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SUMMARY

The discussion centers on calculating the standard deviation for a sample of batteries with an average voltage of 60 volts and a population standard deviation of 4 volts. For Problem A, the standard deviation of the total voltage of 9 batteries is calculated as 12 volts using the formula sqrt(9 * 4^2). In contrast, Problem B calculates the standard deviation of the average voltage as 1.3333 volts by dividing the population standard deviation by the square root of the sample size (sqrt(9)). The distinction between total and average variance is emphasized, highlighting the need to apply different formulas for each scenario.

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Homework Statement



This was an example but I am not sure why there is a difference in the way they are calculating the standard deviation.

A type of battery is produced with an average voltage of 60 with a standard deviation of 4 volts.

A: If 9 batteries are selected at random, what is the probability that the total voltage of the 9 batteries is greater than 530?
B: What is the probability that the average voltage of the 9 batteries is less than 62?


Homework Equations





The Attempt at a Solution



Problem A: For the stdev they just: sqrt( 9 * 4^2) = 12

Problem B: For the stdev they just: 4/sqrt(9) = 1.3333

I get why Problem B is the way it is. We are dealing with a sample and we have the population stdev and we need to approximate the sample standard deviation by dividing by sqrt(n). But for Problem A, I feel like I am missing something simple. Any clarification would be great.
 
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USN2ENG said:

Homework Statement



This was an example but I am not sure why there is a difference in the way they are calculating the standard deviation.

A type of battery is produced with an average voltage of 60 with a standard deviation of 4 volts.

A: If 9 batteries are selected at random, what is the probability that the total voltage of the 9 batteries is greater than 530?
B: What is the probability that the average voltage of the 9 batteries is less than 62?


Homework Equations





The Attempt at a Solution



Problem A: For the stdev they just: sqrt( 9 * 4^2) = 12

Problem B: For the stdev they just: 4/sqrt(9) = 1.3333

I get why Problem B is the way it is. We are dealing with a sample and we have the population stdev and we need to approximate the sample standard deviation by dividing by sqrt(n). But for Problem A, I feel like I am missing something simple. Any clarification would be great.

The total and the average have different variances. Go back and review your formulas.
 
V[9X] = 81 * V[X] = 81 * (1.33333) = 144 and then the stdev = 12

Sorry, for some reason I had never put that together.
 

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