Respuesta :
Answer:
Part (a): The mean of the distribution is 2.
Part (b): The standard deviation of the distribution is 1.525
Step-by-step explanation:
Consider the provided information.
Part (a) What is the mean of the distribution?
The mean of the sampling distribution of [tex](\bar x_1 -\bar x_2)[/tex] is (µ₁ − µ₂).
It is given that μ₁ = 31, σ₁ = 3, μ₂ = 29, and σ₂ = 2.
Mean of distribution = (x₁ - x₂)
Mean of distribution = (31 - 29) = 2
Hence, the mean of the distribution is 2.
Part (b) What is the standard deviation of the distribution?
If the two samples are independent, the standard deviation of the sampling distribution is: [tex]\sigma_{(x_1-x_2)}=\sqrt{\left(\dfrac{\sigma^2_1}{n_1}+\dfrac{\sigma^2_2}{n_2}\right)}}[/tex]
Substitute the respective values in the above formula.
[tex]\sigma_{(x_1-x_2)}=\sqrt{\left(\dfrac{3^2}{4}+\dfrac{2^2}{53}\right)}}[/tex]
[tex]\sigma_{(x_1-x_2)}=\sqrt{\left(\dfrac{9}{4}+\dfrac{4}{53}\right)}}[/tex]
[tex]\sigma_{(x_1-x_2)}\approx1.525[/tex]
Hence, the standard deviation of the distribution is 1.525
