Question

question 16 (4 points)
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select all of the values for the population mean that would be plausible based on an estimate of 105 cm with a margin of error of 21 cm.
105 cm
76 cm
87 cm
113 cm
154 cm

Explanation:

Step1: Find the confidence interval

The formula for the confidence interval is \( \text{Estimate} - \text{Margin of Error} \leq \mu \leq \text{Estimate} + \text{Margin of Error} \).
Substitute the given values: \( 105 - 21 \leq \mu \leq 105 + 21 \).
Calculate the bounds: \( 84 \leq \mu \leq 126 \).

Step2: Check each value

• 105 cm: \( 84 \leq 105 \leq 126 \), so plausible.
• 76 cm: \( 76 < 84 \), not plausible.
• 87 cm: \( 84 \leq 87 \leq 126 \), so plausible.
• 113 cm: \( 84 \leq 113 \leq 126 \), so plausible.
• 154 cm: \( 154 > 126 \), not plausible.

Answer:

The plausible values are 105 cm, 87 cm, 113 cm. So the selected options are:

• 105 cm
• 87 cm
• 113 cm