People at an airport can pass through security on one of two levels: level A or level B. Suppose that, on average, it takes people
22
2222 minutes to pass through security on level A with a standard deviation of
7
77 minutes. On level B, the mean and standard deviation are
20
2020 and
6
66 minutes, respectively.
Every day, the airport looks at an SRS of
100
100100 people who use level A, and an independent SRS of
150
150150 people who use level B. They calculate the mean time for each sample, then look at the difference
(
A
−
B
)
(A−B)left parenthesis, start text, A, end text, minus, start text, B, end text, right parenthesis between the sample means.
What are the mean and standard deviation (in minutes) of the sampling distribution of the difference in sample means?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
μ
x
ˉ
A
−
x
ˉ
B
=
2
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
+
6
2
250

μ
x
ˉ

A
​
−
x
ˉ

B
​

​

σ
x
ˉ

A
​
−
x
ˉ

B
​

​

​

=2
=
250
7
2
+6
2

​

​

​


(Choice B)
B
μ
x
ˉ
A
−
x
ˉ
B
=
2
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
100
+
6
2
150

μ
x
ˉ

A
​
−
x
ˉ

B
​

​

σ
x
ˉ

A
​
−
x
ˉ

B
​

​

​

=2
=
100
7
2

​
+
150
6
2

​

​

​


(Choice C)
C
μ
x
ˉ
A
−
x
ˉ
B
=
21
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
+
6
2
250

μ
x
ˉ

A
​
−
x
ˉ

B
​

​

σ
x
ˉ

A
​
−
x
ˉ

B
​

​

​

=21
=
250
7
2
+6
2

​

​

​


(Choice D)
D
μ
x
ˉ
A
−
x
ˉ
B
=
21
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
100
+
6
2
150

μ
x
ˉ

A
​
−
x
ˉ

B
​

​

σ
x
ˉ

A
​
−
x
ˉ

B
​

​

​

=21
=
100
7
2

​
+
150
6
2

​

​

​