Constructing a Confidence Interval for a Population Mean A biologist measures the lengths of a random sample 30 mature brown trout in a large lake and finds that the sample a mean weight of 41 pounds. Assume the population standard deviation is 3.7 pounds. Based on this, construct a 90% confidence interval for the mean weight of all mature brown trout in the lake. Round your anwers to two decimal places. <μ

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**Constructing a Confidence Interval for a Population Mean**

A biologist measures the lengths of a random sample of 30 mature brown trout in a large lake and finds that the sample has a mean weight of 41 pounds. Assume the population standard deviation is 3.7 pounds. Based on this, construct a 90% confidence interval for the mean weight of all mature brown trout in the lake.

Round your answers to two decimal places.

\[
\underline{\hspace{2cm}} \quad < \quad \mu \quad < \quad \underline{\hspace{2cm}}
\]
Transcribed Image Text:**Constructing a Confidence Interval for a Population Mean** A biologist measures the lengths of a random sample of 30 mature brown trout in a large lake and finds that the sample has a mean weight of 41 pounds. Assume the population standard deviation is 3.7 pounds. Based on this, construct a 90% confidence interval for the mean weight of all mature brown trout in the lake. Round your answers to two decimal places. \[ \underline{\hspace{2cm}} \quad < \quad \mu \quad < \quad \underline{\hspace{2cm}} \]
Expert Solution
Step 1

Given:

Sample size n = 30

Sample mean X = 41

Population standard deviation σ = 3.7

Confidence level = 90%

Formula Used:

Confidence Interval = X ± Zα/2σn

 

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