The table to the right lists probabilities for the corresponding numbers of girls in three births. What is the random variable, what are its possible values, and are its values numerical?
Number of Girls x P(x)
0 0.125
1 0.375
2 0.375
3 0.125
a) The rando
c) The random variable is x, which is the number of girls in three births. The possible values of x are 0, 1, 2, and 3. The values of the random value x are numerical.
Is the random variable given in the accompnaying table discrete or continuous? Explain.
Number of Girls, x P(x)
0 0.063
1 0.250
2 0.375
3 0.250
4 0.063
The random variable given in the accompanying table is __________ because __________.
The random variable given in the accompanying table is _discrete_ because _there are a finite number of values_.
For 100 births, P(exactly 58 girls) = 0.0223 and P(58 or more girls) = 0.067. Is 58 girls in 100 births a significanlty high number of girls? Which probability is relevant to answerting that question? Consider a number of girls to be significantly high if
The relevant probability is _P(58 or more girls),_ so 58 girls in 100 births _is not_ a significantly high number of girls because the relevant probability is _greater than_ 0.05.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
The number of fish caught during a fishing tournament.
a) It is continuous random variable.
b) It is a discrete random variable.
c) It is not
b) It is discrete random variable.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
The number of textbook authors now sitting at a computer.
a) It is continuous random variable.
b) It is a discrete random variable.
c) It is n
b) It is a discrete random variable.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
The political party affiliation of adults in the United States.
a) It is continuous random variable.
b) It is a discrete random variable.
c) I
c) It is not a random variable.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
The number of points scored during a basketball game.
a) It is continuous random variable.
b) It is a discrete random variable.
c) It is not a
b) It is a discrete random variable.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
The distance a baseball travels in the air after being hit.
a) It is continuous random variable.
b) It is a discrete random variable.
c) It is
a) It is continuous random variable.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
The time it takes to fly from City A to City B.
a) It is continuous random variable.
b) It is a discrete random variable.
c) It is not a rando
a) It is continuous random variable.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
The weight of a hamburger.
a) It is continuous random variable.
b) It is a discrete random variable.
c) It is not a random variable.
a) It is continuous random variable.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
The hair color of adults in the United States.
a) It is continuous random variable.
b) It is a discrete random variable.
c) It is not a random
c) It is not a random variable.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
The number of runs scored during a baseball game.
a) It is continuous random variable.
b) It is a discrete random variable.
c) It is not a ran
b) It is a discrete random variable.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
The number of people in a resturant that has a capacity of 200.
a) It is continuous random variable.
b) It is a discrete random variable.
c) I
b) It is a discrete random variable.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
The time it takes to drive from City A to City B.
a) It is continuous random variable.
b) It is a discrete random variable.
c) It is not a ran
a) It is continuous random variable.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable.
The distance a football travels in the air after bring thrown.
a) It is continuous random variable.
b) It is a discrete random variable.
c) It
a) It is continuous random variable.
Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probabilityy distributi
a) Yes, the table shows a probability distribution.
a) u=_2.5_child(ren)
0x0.029+1x0.159+2x0.312+3x0.312+4x0.159+5x0.029=2.5
a) o = _1.1_ child(ren)
(0-2.5)^2x0.029+(1-2.5)^2x0.159+(2-2.5)^2x0.312+(3-2.5)^2x0.312+(4-2.5)^2x0.159+(5-2.5)^2x0.029=1.234
Take
When conducting research on color blindness in males, a researcher forms random groups with five males in each group. The random variable x is the the number of males in the group who have a form of color blindness. Deteremine whether a probability distri
a) Yes, the table shows a probability distribution.
a) u=_0.4_ male(s)
0.665+1
0.277+2
0.052+3
0.005+4
0.001+5
0.000=0.4
a) o=_0.6_ male(s)
(0-0.4)^2
0.665+(1-0.4)^2
0.277+(2-0.4)^2
0.052+(3-0.4)^2
0.005+(4-0.4)^2
0.001+(5-0.4)^2
0.000=0.386
Take sq. rt.
Ted is not particularly creative. He uses the pickup line "If I could rearrange the alphabet, I'd put U and I together." The random variable x is the number of women Ted approaches before encountering one who reacts positively. Determine whether a probabi
e) No, the sum of all probabilities is not equal to 1.
b) The table does not show a probability variable.
b) The table does not show a probability variable.
A sociologist randomly selects single adults for different groups of three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. Determine wheather a probability distribution is given. If a probability
a) Yes, the table shows a probability distribution.
a) u=_1.6_ adult(s)
0.086+1
0.339+2
0.421+3
0.154=1.6
a) o=_0.8_ adult(s)
(0-1.6)^2
0.086+(1-1.6)^2
0.339+(2-1.6)^2
0.421+(3-1.6)^2
0.154=0.7114
Take sq rt of 0.7114=0.8
Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a? self-driving vehicle. Determine whether a probability distribution is given. If a proba
a) Yes, the table shows a probability distribution.
a) u=_0.9_ adult(s)
0.365+1
0.425+2
0.183+3
0.027=0.9
a) o=_0.8_ adult(s)
(0-0.9)^2
0.365+(1-0.9)^2
0.425+(2-0.9)^2
0.183+(3-0.9)^2
0.027=0.6404
Find sq rt. of 0.6404=0.8
Refter to the acoompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and the standard deviation for the number of girls in
The mean is u=_4.0_ girl(s).
0.004+1
0.025+2
0.111+3
0.228+4
0.281+5
0.211+6
0.102+7
0.033+8*0.005=4.0
The standard deviation is o=_1.4_ girl(s)
(0-4.0)^2
0.004+(1-4.0)^2
0.025+(2-4.0)^2
0.111+(3-4.0)^2
0.228+(4-4.0)^2
0.281+(5-4.0)^2
0.211+(6-4.0)^2
0.10
The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl in 10 births is a signific
The maximum value in this range is _8.4_ girls.
u+2o=maximum value
The minimum value in this range is _1.6_ girls.
u-2o=minimum value
b) Yes, 1 girl is a significantly low number of? girls, because 1 girl is below the range of
The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts? 1-3 below.
Number of Girls x P(x)
0 0.004
1 0.033
2 0.118
3 0.224
4 0
1. Find the probability of getting exactly 6 girls in 8 births. _0.118_
P(x) in row 6
2. Find the probability of getting 6 or more girls in 8 births. _0.155_
P(x) of row 6-8 added together.
d) The result from part? b, since it is the probability of the gi
The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts 1-4 below.
Number of Girls x P(x)
0 0.003
1 0.025
2 0.116
3 0.211
4 0.
1. Find the probability of getting exactly 1 girl in 8 births. _0.025_
P(x) in row 1.
2. Find the probability of getting 1 or fewer girls in 8 births. _0.028_
P(x) of row 1 and 0 added together.
a) Since getting 0 girls is an even lower number of girls th
Refer to the accompanying? table, which describes the number of adults in groups of five who reported sleepwalking. Find the mean and standard deviation for the numbers of sleepwalkers in groups of five.
x P(x)
0 0.186
1 0.357
2 0.307
3 0.115
4 0.033
5 0.
The mean is _1.5_ sleepwalker(s).
0.186+1
0.357+2
0.307+3
0.115+4
0.033+5
0.002=1.5
The standard deviation is _1.0_ sleepwalker(s).
(0-1.5)^2
0.0186+(1-1.5)^2
0.357+(2-1.5)^2
0.307+(3-1.5)^2
0.115+(4-1.5)^2
0.033+(5-1.5)^2
0.002=1.074
Take sq rt of 1.074=
The accompanying table describes the random variable? x, the numbers of adults in groups of five who reported sleepwalking. Complete parts? (1) through? (4) below.
x P(x)
0 0.157
1 0.438
2 0.252
3 0.115
4 0.031
5 0.007
1. Find the probability of getting e
1. Find the probability of getting exactly 4 sleepwalkers among 5 adults. _0.031_
P(x) for row 4 = 0.031
2. Find the probability of getting 4 or more sleepwalkers among 5 adults. _0.038_
P(x) for row 4 & 5 added together = 0.038
d) Since the probability o
In a state's Pick 3 lottery game, you pay $1.29 to select a sequence of three digits (from 0 to 9), such as 577. If you select the same sequence of three digits that are draw, you win and collect $309.82. Complete parts (a) through (e).
a) How many differ
a) How many different selections are possible? _1000_
10^3=1000
b) What is the probability of winning? _0.001_
1/1000=0.001
c) If you win, what is your net profit? _$308.53_
$309.82-$1.29=$308.53
d) Find the expected value. _-0.98_
$308.53(1/1000)-$1.29(9
When playing roulette at a casino, a gambler is trying to decide whether to bet $10 on the number 31 or to bet $10 that the outcome is any one of the three possibilitiies 00, 0, or 1. The gambler knows that the expected value of the $10 bet for a single n
The expected value is _$-6.05_.
(3/38)
40-(35/38)
10=$-6.05
Since the expected value of the bet on the number 31 is _greater_ than the expected value for the bet that the outcome is 00, 0, or 1, the bet on _the single number_ is better.
Thre is a 0.9987 probability that a randomly selected 33-year-old male lives through the year. A life insurance company charges $167 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $110,000
The value corresponding to surviving the year is _$-167_.
The value corresponding to not surviving the year is _$109833_.
$110,000-$167=$109833
The expected value is _$-24.00_.
0.9987
-167+(1-0.9987)
110000=-23.78 Round to $-24.00
_Yes_, because the insur
A __________ variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.
A _random_ variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.
A __________ random variable has either a finite or a countable number of values.
A _discrete_ random variable has either a finite or a countable number of values.
A __________ random variable has infinitely many values assoicated with measurements.
A _continuous_ random variable has infinitely many values assoicated with measurements.
In a probability histogram, there is a correspondence between __________.
In a probability histogram, there is a correspondence between _area and probability_.
If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct. This represents the __________.
If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct. This represents the _Rare Event Rule_.
The __________ of a discrete random variable represents the mean value of the outcomes.
The _expected value_ of a discrete random variable represents the mean value of the outcomes.