PLEASE SOLVE WITH CLEAR EXPLANATIONS

1.Two of the following statements describe a correct probability model. Which statement doesnot?

A.There is a probability assigned to each event.

B.The sum of all the probabilities is equal to one.

C.All of the probabilities are between negative one and one.

2.Which of the following random variables is continuous?

A.Time required to run a mile

B.Number of children in a family

C.Number of books on a shelf

3.Here are four possible probability distributions for the number of cars owned by a family. Which one is a correct probability distribution?

A.

X= number of cars	0	1	2	3	4
Pr(X=x)	0.1	0.3	0.4	0.2	0.1

B.

X= number of cars	0	1	2	3	4
Pr(X=x)	0.0	0.2	0.4	0.3	0.1

C.

X= number of cars	0	1	2	3	4
Pr(X=x)	0.5	0.45	0.6	0.25	0.2

D.

X= number of cars	0	1	2	3	4
Pr(X=x)	0.2	0.3	1.2	0.45	0.15

A couple decides to have two children. Write out each possible combination of boys and girls. For example, the couple could have a boy first and then a girl, which would be written BG.

4.How many distinct combinations are possible?

A.2

B.3

C.4

D.5

5.Which of the following shows the correct probability distribution for the number of boys they might have?

A.

X= number of boys	0	1	2
Pr(X=x)	0.25	0.5	0.25

B.

X= number of boys	0	1	2
Pr(X=x)	0.33	0.33	0.33

C.

X= number of boys	0	1	2
Pr(X=x)	0.0	0.5	0.5

6.A different couple decides to have 3 children. The probability distribution for the number of girls they might have is shown below.

X= number of girls	0	1	2	3
Pr(X)	0.125	0.375	0.375	0.125

What is the probability the couple has at least one girl?

A.0.125

B.0.375

C.0.5

D.0.625

E.0.875

ACT scores are Normally distributed with a mean of 21 and a standard deviation of 6. SAT scores are Normally distributed with a mean of 510 and a standard deviation of 100. Emma scored 646 on the SAT and Tess scored 26 on the ACT.

7.Who has the better score?

A.Emma

B.Tess

8.What is the probability that a randomly selected student scored lower than 33 on the ACT?

A.0.025

B.0.840

C.0.975

D.0.9985