Question

An argonomist measured the heights of n corn plants. The mean height was 220 cm, and the standard deviation was 15 cm. Calculate the standard error of the mean for a sample size of 100.

Answer 1

Answer:

The standard error of the mean for a sample size of 100 is 1.5.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation, which is also called standard error, $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\sigma = 15$

Calculate the standard error of the mean for a sample size of 100.

This is s when n = 100. So

$s = \frac{15}{\sqrt{100}} = 1.5$

The standard error of the mean for a sample size of 100 is 1.5.