Suppose that the raw daily oxygen purities delivered by an air-products supplier have a standard deviation LaTeX: \sigma\approx.1 σ ≈ .1 (percent), and it is plausible to think of daily purites as independent random variables. Approximate the probability that the sample mean LaTeX: \frac{ }{X} X of n = 25 delivered purities falls within .03 (percent) of the raw daily purity mean, LaTeX: \mu μ .

There is a probability of 86.6% that the sample mean falls within 0.03 percent of the raw purity mean.

Step-by-step explanation:

We have a population standard deviation of σ ≈ 0.1.

We have a sample of size n=25.

Then, we have a sampling distribution, which has a standard deviation for the sample mean that is:

Now, we can calculate a z-score for a deviation of 0.03 percent from the mean as:

Note: we considered that the margin is ±0.03.

Then, the probability is:

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus

what chart am i supposed to follow?