Two Independent Random Samples Are Drawn from Two Normal Populations

question 34

Short Answer

Two independent random samples are drawn from two normal populations. The sample sizes are 20 and 25, respectively. The parameters of these populations are: $$\begin{array} { | l | l | } \hline \text { Population 1: } & \mu = 505 , \sigma = 10 \\\hline \text { Population } 2 : & \mu = 475 , \sigma = 7 \\\hline\end{array}$$ Find the probability that the difference between the two sample means $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is between 25 and 35.

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Definitions:

Genetic Program

The set of instructions encoded in the DNA of an organism that directs the development, functioning, and reproduction of that organism.

Developmental Norm

A benchmark in child development that outlines typical milestones or behaviors at various ages.

Achieves

Accomplishes or succeeds in bringing about a desired result or reaching a target.

Deformities

Abnormalities in the form or shape of a part of the body, often resulting from genetic factors, trauma, or disease.