Calculating Standard Deviation for a Sample of Batteries

[USN2ENG]

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.

 

[Ray Vickson]

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.

 

[USN2ENG]

V[9X] = 81 * V[X] = 81 * (1.33333) = 144 and then the stdev = 12

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