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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

Two Independent Random Samples Are Drawn from Two Normal Populations