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?
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 accompanying table discrete
or? continuous? Explain.
The random variable given in the accompanying table is
discrete
because
there are a finite number of values.
For 100? births, P(exactly 55 ?girls)equals0.0485 and ?P(55 or more ?girls)equals0.184. Is 55 girls in 100 births a significantly high number of? girls? Which probability is relevant to answering that? question? Consider a number of girls to be significan
The relevant probability is
P(55 or more girls),
so 55 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.
a. The number of hits to a website in a day
b. The number of light bulbs that burn out in the next week in a room with 17 bulbs
c. The gende
a. It is a discrete random variable.
b. It is a discrete random variable.
c. It is not a random variable.
d. It is a discrete random variable.
e. It is a discrete random variable.
f. It is a continuous random variable.
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 associated with measurements.
A
continuous
random variable has infinitely many values associated 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.
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 probability distribut
Yes, the table shows a probability distribution.
muequals
2.5 ?child(ren)
sigmaequals
1.1 ?child(ren)
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 number of males in the group who have a form of color blindness. Determine whether a probability distributi
?Yes, the table shows a probability distribution
muequals
0.4 ?male(s)
sigmaequals
0.6 ?male(s)
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 prob
?No, the sum of all the probabilities is not equal to 1.
The table does not show a probability distribution.
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 whether a probability distribution is given. If a probability
?Yes, the table shows a probability distribution.
muequals
1.6 ?adult(s)
sigmaequals
0.8 ?adult(s) ?
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
yes
.9
.8
Refer to the accompanying? 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 standard deviation for the number of girls in 8 bi
The mean is muequals
4 ?girl(s).
The standard deviation is sigmaequals
1.4 ?girl(s).
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.
The mean is
1.5 ?sleepwalker(s). ?
The standard deviation is
1.0 ?sleepwalker(s).
Based on a? survey, assume that 57?% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when five consumers are randomly? selected, exactly three of them are comfortable with the drones. What i
There are other arrangements consisting of three consumers who are comfortable and two who are not. The probabilities corresponding to those other arrangements should also be included in the result.
Based on a? survey, assume that 28?% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when four consumers are randomly? selected, exactly two of them are comfortable with delivery by dro
The value of n is
4.
?(Type an integer or a decimal. Do not? round.)
The value of x is
2.
?(Type an integer or a decimal. Do not? round.)
The value of p is
0.28.
?(Type an integer or a decimal. Do not? round.)
The value of q is
0.72.
?(Type an integer or
A Gallup poll of 1236 adults showed that? 12% of the respondents believe that it is bad luck to walk under a ladder. Consider the probability that among 30 randomly selected people from the 1236 who were? polled, there are at least 2 who have that belief.
Yes. Although the selections are not? independent, they can be treated as being independent by applying the? 5% guideline.
Based on a? survey, when 1009 consumers were asked if they are comfortable with drones delivering their? purchases, 42% said yes. The probability of randomly selecting 30 of the 1009 consumers and getting exactly 24 who are comfortable with the drones is
The probability 0plus indicates that the probability is a very small positive value. It indicates that the event is? possible, but very unlikely.
Which of the following is not a requirement of the binomial probability? distribution?
The trials must be dependent.
If calculations are? time-consuming and if a sample size is no more than? 5% of the size of the? population, the? _______ states to treat the selections as being independent? (even if the selections are technically? dependent).
If calculations are? time-consuming and if a sample size is no more than? 5% of the size of the? population, the
5% Guideline for Cumbersome Calculations
states to treat the selections as being independent? (even if the selections are technically? depende
In the binomial probability? formula, the variable x represents the? _______.
In the binomial probability? formula, the variable x represents the
number of successes.
Which of the following is NOT one of the three methods for finding binomial probabilities that is found in the chapter on discrete probability? distributions?
Use a simulation
For the binomial? distribution, which formula finds the standard? deviation?
//npq
A main goal in statistics is to interpret and understand the meaning of statistical values. The? _______ can be very helpful in understanding the meaning of the mean and standard deviation.
A main goal in statistics is to interpret and understand the meaning of statistical values. The
Range Rule of Thumb
can be very helpful in understanding the meaning of the mean and standard deviation.
Identify the expression for calculating the mean of a binomial distribution.
np
Based on a? survey, assume that 59?% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when four consumers are randomly? selected, exactly two of them are comfortable with the drones. What is
There are other arrangements consisting of two consumers who are comfortable and two who are not. The probabilities corresponding to those other arrangements should also be included in the result
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? (a) through? (d) below.
c. Since the probability of getting 7 or 8 girls includes getting 6? girls, the result from part? (b) is the relevant probability.
d. No, since the appropriate probability is greater than? 0.05, it is not a significantly high numbe
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? (a) through? (d) below.
Find the probability of getting exactly 1 gir
c. Since getting 0 girls is an even lower number of girls than getting 1? girl, the result from part? (b) is the relevant probability.
d. Yes, since the appropriate probability is less than? 0.05, it is a significantly low number.
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
Use the range rule of thumb to identify a range of values that are not significant.
The maximum value in this range is
8.3 girls.
?(Round to one decimal place as? needed.)
The minimum value in this range is
1.6 girls.
?(Round to one decimal place as? need
The accompanying table describes the random variable? x, the numbers of adults in groups of five who reported sleepwalking. Complete parts? (a) through? (d) below.
Find the probability of getting exactly 4 sleepwalkers among 5 adults
c.
Since the probability of getting 5 sleepwalkers includes getting 4? sleepwalkers, the result from part? (b) is the relevant probability.
d.
?Yes, since the appropriate probability is less than? 0.05, it is a significantly high number.
Determine whether the given procedure results in a binomial distribution. If it is not? binomial, identify the requirements that are not satisfied.
Recording the genders of 50 people in a statistics class nothing
A.
Yes comma because all 4 requirements are satisfied.
Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer.
An experimental drug is administered to 160 randomly selected? individuals, with the number of individuals responding favorably
A.
?Yes, because the experiment satisfies all the criteria for a binomial experiment.
Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer.
Five cards are selected from a standard? 52-card deck without replacement. The number of fours selected is recorded.
Does the p
?No, because the trials of the experiment are not independent and the probability of success differs from trial to trial.
Determine whether or not the procedure described below results in a binomial distribution. If it is not? binomial, identify at least one requirement that is not satisfied.
Five hundred different voters in a region with two major political? parties, A and?
.
Yes comma the result is a binomial probability distribution.
Determine whether the given procedure results in a binomial distribution. If it is not? binomial, identify the requirements that are not satisfied.
Treating 150 bald men with a special shampoo and recording how they say their scalp feels
Choose the correc
No comma because there are more than two possible outcomes.
?Multiple-choice questions each have four possible answers left parenthesis a comma b comma c comma d right parenthesis?, one of which is correct. Assume that you guess the answers to three such questions.
a. Use the multiplication rule to find ?P(WCW?),
...
Multiple-choice questions each have five possible answers left parenthesis a comma b comma c comma d comma e right parenthesis?, one of which is correct. Assume that you guess the answers to three such questions.
a. Use the multiplication rule to find ?P(
...
n a? state's Pick 3 lottery? game, you pay ?$0.95 to select a sequence of three digits? (from 0 to? 9), such as 300. If you select the same sequence of three digits that are? drawn, you win and collect ?$361.43. Complete parts? (a) through? (e).
a. How many different selections are? possible?
1000
b. What is the probability of? winning?
0.001 ?(Type an integer or a? decimal.)
c. If you? win, what is your net? profit?
e. If you bet $ 0.95 in a certain? state's Pick 4? game, the expected value is n
...
Since the expected value of the bet on the number 26 is
greater
than the expected value for the bet that the outcome is 00 comma 0 comma or 1?, the bet on
the single number
is better.
Based on a? poll, 60?% of adults believe in reincarnation. Assume that 6 adults are randomly? selected, and find the indicated probability. Complete parts? (a) through? (d) below.
calc binompdf
a. What is the probability that exactly 5 of the selected adults believe in? reincarnation?
The probability that exactly 5 of the 6 adults believe in reincarnation is
0.187.
?(Round to three decimal places as? needed.)
b. What is the probability that all
When purchasing bulk orders of? batteries, a toy manufacturer uses this acceptance sampling? plan: Randomly select and test 50 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not mee
The probability that this whole shipment will be accepted is
0.9216.
?(Round to four decimal places as? needed.)
The company will accept
92.16?% of the shipments and will reject
7.84?% of the? shipments, so
almost all of the shipments will be accepted.