Question

a simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be 138, with a standard deviation of 34. what is the 90% confidence interval for the population mean? use the table below to help you answer the question.

\

$$\begin{tabular}{|c|c|c|c|} \\hline confidence level & 90\\% & 95\\% & 99\\% \\\\ \\hline z*-score & 1.645 & 1.96 & 2.58 \\\\ \\hline \\end{tabular}$$

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

(a) 128.75 to 147.25
(b) 130.98 to 145.02
(c) 132.10 to 143.90
(d) 137.38 to 138.62

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

$$
LATEXBLOCK1
$$

Construct the confidence interval

Using the Confidence Interval Construction knowledge point

$$
LATEXBLOCK2
$$

Answer:

• 128.75 to 147.25
• 130.98 to 145.02
• 132.10 to 143.90 (Correct answer)
• 137.38 to 138.62