Question

a survey of 35 individuals who passed the seven exams and obtained the rank of fellow in the actuarial field finds the average salary to be $150,000. if the standard deviation for the population is $15000, construct a 95% confidence interval for all fellows. note: 1. write your answer with a $ as an ordered pair- round to the nearest integer- example (23, 5). 2. do not use commas in your numbers- just write the digits- example 125856.

Explanation:

Step1: Find the z - value

For a 95% confidence interval, the z - value \(z_{\alpha/2}\) is 1.96.

Step2: Calculate the margin of error \(E\)

The formula for the margin of error when the population standard deviation \(\sigma\) is known is \(E = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\).
Given \(n = 35\), \(\sigma=15000\), and \(z_{\alpha/2}=1.96\).

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Step3: Calculate the confidence interval

The confidence interval formula is \(\bar{x}-E<\mu <\bar{x} + E\), where \(\bar{x}=150000\)

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Answer:

\((145030,154970)\)