Question

use the range rule of thumb to identify the values that are significantly low, the values that are significantly high, and the values that are neither significantly low nor significantly high. a test is used to assess readiness for college. in a recent year, the mean test score was 22.7, and the standard deviation was 5.1. identify the test scores that are significantly low or significantly high. what test scores are significantly low? select the correct answer below and fill in the answer box(es) to complete your choice. a. test scores that are greater than \boxed{}. (round to one decimal place as needed) b. test scores that are less than 12.5. (round to one decimal place as needed.) c. test scores that are between \boxed{} and \boxed{}. (round to one decimal place as needed. use ascending order.) what test scores are significantly high? select the correct answer below and fill in the answer box(es) to complete your choice. a. test scores that are greater than \boxed{}. (round to one decimal place as needed) b. test scores that are less than \boxed{}. (round to one decimal place as needed.) c. test scores that are between \boxed{} and \boxed{}. (round to one decimal place as needed. use ascending order.)

Explanation:

Step1: Recall the range rule of thumb for significant values

The range rule of thumb states that values are significantly low if they are less than $\mu - 2\sigma$ and significantly high if they are greater than $\mu + 2\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation. Values between $\mu - 2\sigma$ and $\mu + 2\sigma$ are neither significantly low nor high.

Given $\mu = 22.7$ and $\sigma = 5.1$.

Step2: Calculate the lower bound ($\mu - 2\sigma$)

First, calculate $2\sigma$: $2\times5.1 = 10.2$

Then, $\mu - 2\sigma = 22.7 - 10.2 = 12.5$

Step3: Calculate the upper bound ($\mu + 2\sigma$)

$\mu + 2\sigma = 22.7 + 10.2 = 32.9$

For "What test scores are significantly low?"

Using the range rule, significantly low scores are less than $\mu - 2\sigma = 12.5$. So the correct option is B: Test scores that are less than $12.5$.

For "What test scores are neither significantly low nor high?"

These are scores between $\mu - 2\sigma$ and $\mu + 2\sigma$, i.e., between $12.5$ and $32.9$. So the correct option is C (assuming option C is the one with the range, but from the given, the option C for neither would be between $12.5$ and $32.9$).

For "What test scores are significantly high?"

Significantly high scores are greater than $\mu + 2\sigma = 32.9$. So the correct option is A: Test scores that are greater than $32.9$.

Answer:

s:

• Significantly low: B. Test scores that are less than $12.5$
• Neither significantly low nor high: C. Test scores that are between $12.5$ and $32.9$ (assuming option C is structured this way)
• Significantly high: A. Test scores that are greater than $32.9$