Question

1. katherine recorded the weekly number of hours she worked at her summer job. if the mean of the data is 20 with a standard deviation of 5.7, circle all values that fall within one standard deviation of the mean. {9, 14, 18, 20, 23, 24, 25, 27}

Explanation:

Step1: Find the lower bound

The lower bound within one standard deviation of the mean is calculated by subtracting the standard deviation from the mean. So, \( 20 - 5.7 = 14.3 \).

Step2: Find the upper bound

The upper bound within one standard deviation of the mean is calculated by adding the standard deviation to the mean. So, \( 20 + 5.7 = 25.7 \).

Step3: Identify values in the range

Now we check which values from the set \(\{9, 14, 18, 20, 23, 24, 25, 27\}\) lie between \(14.3\) and \(25.7\) (inclusive).

• \(9\): \(9 < 14.3\), so no.
• \(14\): \(14 < 14.3\), so no.
• \(18\): \(14.3 \leq 18 \leq 25.7\), yes.
• \(20\): \(14.3 \leq 20 \leq 25.7\), yes.
• \(23\): \(14.3 \leq 23 \leq 25.7\), yes.
• \(24\): \(14.3 \leq 24 \leq 25.7\), yes.
• \(25\): \(14.3 \leq 25 \leq 25.7\), yes.
• \(27\): \(27 > 25.7\), so no.

Answer:

The values within one standard deviation of the mean are 18, 20, 23, 24, 25.