Q -

A random variable is normally distributed with mean=300 pounds and s=50 pounds. How small can a simple random sample be if the standard error of the mean can be no more than 20 pounds?

Ans:

If s is the standard deviation and n is the sample size, the standard error of the mean is

s/√n

We're looking for n such that

50/√n ≤ 20

√n ≥ 50/20 = 2.5

n ≥ 2.5² = 6.25

Since n is a whole number, round up to n = 7.

You should have some sort of confidence level. 95%? 90? Something else?

The formula for minimum sample size is n=\left(\frac{z\cdot {\sigma}}{E}\right)^{2}

You forgot the z. That is where the confidence level comes in.

With a 95% CI, the minimum sample size is 25