Determine whether or not a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
a) Genetic Disorder
Three males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the three who inherit the X-linked genetic disorder.
x
|
P (x)
|
0
|
0.125
|
1
|
0.375
|
2
|
0.375
|
3
|
0.125
|
b) Caffeine Nation
In the accompanying table, the random variable x represents the number of cups or cans of caffeinated beverages consumed by Americans each day (based on data from the National Sleep Foundation).
x
|
P (x)
|
0
|
0.22
|
1
|
0.16
|
2
|
0.21
|
3
|
0.16
|
c) Overbooked Flights
Air America has a policy of routinely overbooking flights. The random variable x represents the number of passengers who cannot be boarded because there are more passengers than seats (based on data from an IBM research paper by Lawrence, Hong, and Cherrier).
x
|
P (x)
|
0
|
0.051
|
1
|
0.141
|
2
|
0.274
|
3
|
0.331
|
4
|
0.187
|
d) Eye Color
Groups of five babies are randomly selected. In each group, the random variable x is the number of babies
with green eyes (based on data from a study by Dr. Sorita Soni at Indiana University). (The symbol denotes a positive probability value that is very small.)
x
|
P (x)
|
0
|
0.528
|
1
|
0.360
|
2
|
0.098
|
3
|
0.013
|
4
|
0.001
|
5
|
0+
|
e) American Televisions
In the accompanying table, the random variable x represents the number of televisions in a household in the United States (based on data from Frank N. Magid Associates).
x
|
P (x)
|
0
|
0.02
|
1
|
0.15
|
2
|
0.29
|
3
|
0.26
|
4
|
0.16
|
5
|
0.12
|
f) TV Ratings
In a study of television ratings, groups of 6 U.S. households are randomly selected. In the accompanying table, the random variable x represents the number of households among 6 that are tuned to 60 Minutes during the time that the show is broadcast (based on data from Nielsen Media Research).
x
|
P (x)
|
0
|
0.539
|
1
|
0.351
|
2
|
0.095
|
3
|
0.014
|
4
|
0.001
|
5
|
0+
|
6
|
0+
|