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Two Independent Random Samples of 25 Observations Each Are Drawn

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Two independent random samples of 25 observations each are drawn from two normal populations. The parameters of these populations are:  Population 1: μ=150,σ=50 Population 2: μ=130,σ=45\begin{array} { | l | l | } \hline \text { Population 1: } & \mu = 150 , \sigma = 50 \\\hline \text { Population 2: } & \mu = 130 , \sigma = 45 \\\hline\end{array} Find the probability that the mean of sample 1 will exceed the mean of sample 2.

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Definitions:

Itemized List

A list where each entry is separately listed and often numbered or bulleted.

Deposit Slip

A document accompanying a bank deposit, detailing the amount of cash and/or checks being deposited.

Electronic Funds Transfer System

A system that transfers money from one bank account directly to another without any paper money changing hands, often used for payroll, direct deposit, and bill pay services.

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