What is the value of the sample standard deviation?

The width of the confidence interval is 40, so the error about the mean is 20. You have a sample of 25 batteries, so the number of degrees of freedom is 24. The critical t-score for 24 degrees of freedom and a confidence level of .95 is approximately 2.063899.

We can use the t-score to approximate the sample standard deviation:

t = error / (s/sqrt(n))

Solving for s we get

s = error*sqrt(n)/t,

s = 20*sqrt(25)/2.063899

s = 48.45199

its been a while since ive done this stuff so ill do my best to point you in the right direction hopefully. first find the mean which is 460. then the spread would be 480-460= 20. since a confidence interval is centered around of mean, that means you have 2.5% in both tails of the distribution. this corresponds to a value of 1.96. so your spread of 20 is equal to 1.96 standard deviations.

20 = 1.96*s / sqrt 25. solve for s and that should be your standard deviation.

note: the only thing i am unsure about is the t-interval where degrees of freedom come into play. normally a t-interval will have n-1 degrees of freedom so that might change the value of 1.96 to another value. you'll have to look that up in a t-distribution chart.

hope that helps...