Question

a simple random sample of 85 is drawn from a normally distributed population, and the mean is found to be 146, with a standard deviation of 34. which of the following values is outside the 99% confidence interval for the population mean? use the table below to help you answer the question.

remember, the margin of error, me, can be determined using the formula \\(me = \frac{z \cdot s}{\sqrt{n}}\\)

the value of 135 because it is not greater than 136.5
the value of 137 because it is greater than 136.5
the value of 138 because it is less than 153.2
the value of 154 because it is greater than 153.2

Explanation:

Identify the given parameters

Using the Margin of Error Calculation and Confidence Interval Construction knowledge points

$$
LATEXBLOCK0
$$

Calculate the margin of error

Using the Margin of Error Calculation knowledge point

$$
LATEXBLOCK1
$$

Determine the confidence interval limits

Using the Confidence Interval Construction knowledge point

$$
LATEXBLOCK2
$$

The \(99\%\) confidence interval is approximately \([136.5, 155.5]\).

Evaluate the given options

Using the Confidence Interval Construction knowledge point

• The value \(135\) is outside the interval because it is less than \(136.5\) (i.e., not greater than \(136.5\)).
• The value \(137\) is inside the interval.
• The value \(138\) is inside the interval.
• The value \(154\) is inside the interval (since \(154 \le 155.5\)).

Answer:

• the value of 135 because it is not greater than 136.5 (Correct answer)
• the value of 137 because it is greater than 136.5
• the value of 138 because it is less than 153.2
• the value of 154 because it is greater than 153.2