Question

the governor of a state wanted to assess the public education system of the state. she instructed a group of researchers to create a test to assess the knowledge of every high school senior in the state. the researchers administered the tests and found that the average score was 88 points out of 100, with a standard deviation of 28 points. complete parts (a) through (c) below.

μₓ̄ = 88 (type an integer or a decimal.)
σₓ̄ = 1.9 (round to one decimal place as needed.)
c. repeat part (b) for samples of size 450.
μₓ̄ = 88 (type an integer or a decimal.)
σₓ̄ = (round to one decimal place as needed.)

Explanation:

Step1: Recall the formula for the standard deviation of the sample mean

The formula for the standard deviation of the sample mean $\sigma_{\bar{x}}$ is $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size.
Given that $\sigma = 28$ and $n = 450$.

Step2: Substitute the values into the formula

Substitute $\sigma = 28$ and $n = 450$ into the formula:
$$\sigma_{\bar{x}}=\frac{28}{\sqrt{450}}$$
First, calculate $\sqrt{450}\approx21.2132$.
Then, $\frac{28}{21.2132}\approx1.3$.

Answer:

$1.3$