WGU Academy Statistics Module 8 WITH ANSWERS TO ALL QUES.

WGU Academy Statistics Module 8
A couple decides to have children until they have one boy and one girl, but not more
than four children.

The sample space is therefore:

S = {BG, BBG, BBBG, BBBB, GB, GGB, GGGB, GGGG}




A
We are assuming that having a boy or a girl is equally likely[P(B)=P(G)=1/2], and the
that the child's gender in each birth is independent of the gender in the other births.




VI
Let the random variable X be the number of children that the couple will have.




TU
Which of the following is the correct probability distribution of X?

X234
IS
P(X=x) 1/2 1/4 1/4

This is the correct probability distribution, which can be obtained after the following
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summary of outcomes, probabilities, and possible values of X:




A random variable X has a probability distribution of
NA


P(X = x) = (x + 2) / 25 for x = 1, 2, 3, 4, 5.

This tells us that the random variable take the values 1,2,3,4,5, and to find the
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probability of each value, you simply plug-in the value in the formula. For example:

P(X=2) = (2 + 2) / 25 = 4/25

Let's present this probability distribution in a table, and verify that the above
requirements are satisfied.

Substituting x = 1, 2, 3, 4, and 5, respectively, into the formula for P(X = x), we have

,X12345

P(X=x) 3/25 4/25 5/25 6/25 7/25

Clearly, each probability is between 0 and 1. Also, the probabilities sum to (3 + 4 + 5 + 6
+ 7) / 25 = 25/25 = 1.




Based upon data collected in the 2000 United States Census and an expanded number




A
of households, the following histogram was constructed. It shows the distribution of
people per household.




VI
-the number of children in each household.
-the number of people in each household.




TU
-the number of households contacted by the Census.
-the area of each rectangle in the histogram.
-the probabilities for each number of people per household.
the number of people in each household.
IS
Because The variable X (on the horizontal axis) is described above as people per
household.
OM

Recall the following example:
The number of sales that a telemarketing salesperson makes in an hour is a random
variable X having the following probability distribution:
NA


X01234
P(X=x)10/50 12/50 12/50 10/50 6/50
Question 1
This is not a form; we suggest that you use the browse mode and read all parts of the
question carefully.
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What is the probability that the salesperson makes at least one sale in an hour?

12/50
22/50
28/50
40/50
10/50
40/50

, The probability of at least one sale is P(X ≥ 1) = P(X = 1) + P(X = 2) + P(X = 3) + P(X =
4) = (12 + 12 + 10 + 6) / 50 = 40/50, (using the addition principle). Alternatively (and
more efficiently), you can use complements and the fact that the complementary event
of X ≥ 1 is X = 0. Therefore, P(X ≥ 1) = 1 - P(X = 0) = 1 - 10/50 = 40/50.


Given that before the end of an hour the salesperson has made 2 sales already, what is
the probability that he will make less 4 sales?




A
X01234
P(X=x)10/50 12/50 12/50 10/50 6/50




VI
Which of the following represents this probability?
P(X≥2)




TU
P(X<4)
P(X<4|X=2)
P(X≥2|X<4)
P(X<4|X≥2)
IS
P(X<4|X≥2)

We are given that the salesperson has already made 2 sales (X≥2) and we need to find
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the probability that the salesperson makes less than 4 sales (X<4)


Data were collected from a survey given to graduating college seniors on the number of
times they had changed majors. From that data, a probability distribution was
NA


constructed. The random variable X is defined as the number of times a graduating
senior changed majors. It is shown below:

X012345
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P(X=x). 28 .37 .23 .09 .02 .01

What is the probability that a randomly selected student changed his or her major at
least once?

.12

.35