Determine the minimum sample size required when you want to be 75% confident that the sample mean is within 30 units of the population mean assume the population standard deviation of 327.8 in a normally distributed population

The minimum sample size is 158.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

In this question:

The minimum sample size is n.

n is found when M = 30.

We have that

So

Rounding up

The minimum sample size is 158.

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation:

a. 12.5 kg

step-by-step explanation:

f = ma

so

m = f/a = (2500 n)/(200 m/s²) = 12.5 kg

1 n = 1 kg·m/s²