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WGU Academy Statistics Module 8 WITH ANSWERS TO ALL QUES.
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WGU Academy Statistics Module 8 WITH ANSWERS TO ALL QUES. 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} We are assuming that having a boy or a girl is e...

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  • August 20, 2024
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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
OM

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
JP



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.
JP




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
OM

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
JP




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

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