Statistics: sample mean of normal distribution

[musicmar]

Homework Statement

The diameter of a shaft in an optical storage drive is normally distributed N(μ,σ²). The drive specifies that the shaft be 0.2500 ± 0.0015 in. Suppose μ= 0.2508 in and σ = 0.0005 in. What fraction of shafts conform to the design specifications?

The Attempt at a Solution

I am confused with the terminology of this problem. Is 0.2500 the population mean and 0.2508 is the sample mean?
Or is this completely unrelated, and I have to find the probability that a length be between 0.2485 and 0.2515 in?
Some help in getting started would be appreciated.
Thank you!

 

[Ray Vickson]

Homework Statement

The diameter of a shaft in an optical storage drive is normally distributed N(μ,σ²). The drive specifies that the shaft be 0.2500 ± 0.0015 in. Suppose μ= 0.2508 in and σ = 0.0005 in. What fraction of shafts conform to the design specifications?

The Attempt at a Solution

I am confused with the terminology of this problem. Is 0.2500 the population mean and 0.2508 is the sample mean?
Or is this completely unrelated, and I have to find the probability that a length be between 0.2485 and 0.2515 in?
Some help in getting started would be appreciated.
Thank you!

It is crystal clear from the wording that your second interpretation is the correct one. (When I say crystal clear I mean: don't read more into the problem than what it says.)

RGV