The random variable Y is the sum of the dice when two balanced dice are rolled. Its probability distribution is given below. Complete parts a through below. Y 2 3 4 6 7 8 9. 10 11 12 1 P(Y = y) 1 1 1 1 1 1 1 36 18 12 36 36 12 18 36 a. Find and interpret the mean of the random variable. (Type an integer or decimal rounded to three decimal places as needed.)
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Answer the last question for the first picture and the question for the second picture
![The random variable Y is the sum of the dice when two balanced dice are rolled. Its probability distribution is given below. Complete parts a through c
below.
Y
2
4
5
6.
7
8
9
10
11
12
1
P(Y = y)
1
1
1
5
1
36
18
12
36
6.
36
12
18
36
a. Find and interpret the mean of the random variable.
(Type an integer or decimal rounded to three decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff534fa3a-7fc6-4517-a79f-1e1d7853b104%2F5e797763-b05d-4356-933e-c91f43f01d24%2Ffgt1fcp_processed.png&w=3840&q=75)
![A census collected data on everyone that lived in a certain small town. The random variable X is the number of girls out of four children born to a randomly selected couple in that town. Its probability distribution is shown
below. Complete parts a through c.
to
X
2
4
P(X = x)
0.0867
0.2695
0.3673
0.1801
0.0964
c. Construct a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals. Choose the correct histogram below.
A.
В.
D.
Number of Girls
Number of Girls
Number of Girls
Number of Girls
0.5-
0.4-
0.34
0.2-
0.1-
0.5-
0.4-
0.3-
0.2-
01-
0-
0 1 2 3 4
0.5-
0.4-
0.3-
0.2-
0.1-
0-
0 1 2 3 4
0.5-
0.4-
0.3-
0.2-
0.1-
0-
0 1 2 3 4
0 1234
The mean is 1.93
(Type an integer or decimal rounded to four decimal places as needed.)
The one-standard-deviation interval is |, the two-standard-deviation interval is , |, and the three-standard-deviation interval is ||,
(Type integers or decimals rounded to four decimal places as needed. Use ascending order.)
Probability
Probability
Probability
Probability](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff534fa3a-7fc6-4517-a79f-1e1d7853b104%2F5e797763-b05d-4356-933e-c91f43f01d24%2F7g7k7tp_processed.png&w=3840&q=75)
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