A variable of two populations has a mean of 45 and a standard deviation of 24 for one of the populations and a mean of 45 and a standard deviation of 40 for the other population.​ Moreover, the...


A variable of two populations has a mean of 45 and a standard deviation of 24 for one of the populations and a mean of 45 and a standard deviation of 40 for the other population.​ Moreover, the variable is normally distributed on each of the two populations. Complete parts​ (a) through​ (c).


a. For independent samples of size 16 and 25​, respectively, determine the mean and standard deviation of x1−x2.


The mean of x1−x2 is __________

​(Type an integer or a decimal. Do not​ round.)


The standard deviation of x1−x2 is ____________

​(Round to four decimal places as​ needed.



b. Can you conclude that the variable x1−x2 is normally​ distributed? Explain your answer. Choose the correct answer below.






A. ​Yes, since the variable is normally distributed on each of the two​ populations, x1−x2 is normally distributed.





B. ​No, since x1−x2 must be greater than or equal to​ 0, the distribution is right​ skewed, so cannot be normally distributed.





C. Yes, x1−x2 is always normally distributed because of the central limit theorem.





D. ​No, x1−x2 is normally distributed only if the sample sizes are large enough.




c. Determine the percentage of all pairs of independent samples of sizes
16 and 25​, respectively, from the two populations with the property that the difference x1−x2 between the sample means is between −10 and

10.




_________​%




Jun 06, 2022
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