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.

Answer 1

The critical values for a 90% confidence interval are approximately $\pm1.645$, so the confidence interval in this case is roughly

$138\pm1.645\dfrac{34}{\sqrt{90}}=(132.1,143.9)$

Answer 2

Answer:

Step-by-step explanation:

Given that 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.

Confidence level = 90%

Z critical value = 1.645

Sample size n=90

Std error of sample = sigma/sqrt n= 34/9.487

=3.583

Margin of error = ±1.645(3.583)=5.895

Hence confidence interval lower bound = 138-5.895 = 132.105

Upper bound = 138+5.895 = 143.895

Hence confidence interval = (132.11, 143.90)