Chapter 5-1:
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.
In a probability histogram, there is a correspondence between __________.
In a probability histogram, there is a correspondence between _area and probability_.
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) It is not a random variable.
b) It is a discrete random variable.
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.
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 number is -0.53c. For the $10 bet that the outcome is 00, 0, or 1, there is a probability of 3/38 of making a net profit of $40 and a 35/38 probability of losing $10. a) Find the expected value for the $10 bet that the outcome is 00, 0, or 1. The expected value is _____. b) Which bet is better: a $10 bet on the number 31 or a $10 bet that the outcome is any one of the numbers 00, 0, or 1? Why? Since the expected value of the bet on the number 31 is __________ than the expected value for the bet that the outcome is 00, 0, or 1, the bet on __________ is better.
The expected value is _$-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.
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 appropriate probability is 0.05 or less. The relevant probability is __________ so 58 girls in 100 births __________ a significantly high number of girls because the relevant probability is __________ 0.05.
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.
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 as a death benefit. Complete parts (a) through (c) below. a) Fromt he perspective of the 33-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving? The value corresponding to surviving the year is ___________. The value corresponding to not surviving the year is __________. b) If the 33-year-old male purchases the policy, what is the expected value? The expected value is _____. c) Can the insurance company expect to make a profit from many such policies? Why? _____, because the insurance company expects to make an average profit of $_____ on every 33-year-old male it insurance for 1 year.
The value corresponding to surviving the year is _$-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 insurance company expects to make an average profit of $_24.00_ on every 33-year-old male it insurance for 1 year.
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 0.290 5 0.211 6 0.116 7 0.025 8 0.003 1. Find the probability of getting exactly 1 girl in 8 births. _____ 2. Find the probability of getting 1 or fewer girls in 8 births. _____ 3. Which probability is relevant for determining whether 1 is a significantly low number of girls in 8 births: the result from part 1 or part 2? a) Since getting 0 girls is an even lower number of girls than getting 1 girl, the result from part (2) is the relevant probability b) Since the probability of getting more than 1 girl is the complement of the result from part (2), this is the relevant probability. c) Since the probability of getting 1 girl is the result from part (1), this is the relevant probability. d) Since the probability of getting 0 girls is less likely than getting 1 girl, the result from part (1) is the relevant probability. 4) Is 1 a significantly low number of girls in 8 births? Why are why not? Use 0.05 as the threshold for a significant event. a) Yes, since the appropriate probability is less than 0.05, it is a significantly low number. b) No, since the appropriate probability is less than 0.05, it is not a significantly low number. c) Yes, since the appropriate probability is greater than 0.05, it is a significantly low number. d) No, since the appropriate probability is greater than 0.05, it is not a significantly low number.
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 than getting 1 girl, the result from part (2) is the relevant probability a) Yes, since the appropriate probability is less than 0.05, it is a significantly low number.
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 exactly 4 sleepwalkers among 5 adults. _____ 2. Find the probability of getting 4 or more sleepwalkers among 5 adults. _____ 3. Which probability is relevant for determining whether 4 is a significantly high number of sleepwalkers among 5 adults: the result from part (1) or part (2)? a) Since the probability of getting 5 sleepwalkers is less likely than getting 4 sleepwalkers, the result from part (1) is the relevant probability. b) Since the probability of getting fewer than 4 sleepwalkers is the complement of the result from part (2), this is the relevant probability. c) Since the probability of getting 4 sleepwalkers is the result from part (1), this is the relevant probability. d) Since the probability of getting 5 sleepwalkers includes getting 4 sleepwalkers, the result from part (2) is the relevant probability. 4. Is 4 a significantly high number of 4 sleepwalkers among 5 adults? Why or why not? Use 0.05 as the threshold for a significant event. a) Yes, since the appropriate probability is less than 0.05, it is a significantly high number. b) Yes, since the appropriate probability is greater than 0.05, it is a significantly high number. c) No, since the appropriate probability is greater than 0.05, it is not a significantly high number. d) No, since the appropriate probability is less than 0.05, it is not a significantly high number.
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 of getting 5 sleepwalkers includes getting 4 sleepwalkers, the result from part (2) is the relevant probability. a) Yes, since the appropriate probability is less than 0.05, it is a significantly high number.
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 0.242 5 0.224 6 0.118 7 0.033 8 0.004 1. Find the probability of getting exactly 6 girls in 8 births. _____ 2. Find the probability of getting 6 or more girls in 8 births. _____ 3. Which probability is relevant for determining whether 6 is a significantly high number of girls in 8 births: the result from part (a) or part (b)? a) The result from part a, since it less than the probability of the given or more extreme result. b) The result from part b, since it is the complement of the result of part a. c) The result from part a, since it is the exact probability being asked. d) The result from part b, since it is the probability of the given or more extreme result.
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 given or more extreme result.
A __________ random variable has infinitely many values assoicated with measurements.
A _continuous_ random variable has infinitely many values assoicated with measurements.
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.
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 significantly low number of girls. Number of Girls x P(x) 0 0.005 1 0.014 2 0.039 3 0.116 4 0.203 5 0.243 6 0.204 7 0.112 8 0.038 9 0.011 10 0.015 The maximum value in this range is _____ girls. The minimum value in this range is _____ girls. Based on the result, is 1 girl in 10 births a significantly low number of girls? Explain. a) Yes, 1 girl is a significantly low number of girls, because 1 girl is above the range of values that are not significant. b) Yes, 1 girl is a significantly low number of girls, because 1 girl is below the range of values that are not significant. c) No, 1 girl is not a significantly low number of girls, because 1 girl is within the range of values that are not significant.
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
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 0.002 The mean is _____ sleepwalker(s). The standard deviation is _____ sleepwalker(s).
The mean is _1.5_ sleepwalker(s). 0*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=1.0
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 8 births. Number of Girls x P(x) 0 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 The mean is u=_____ girl(s). The standard deviation is o=_____ girl(s)
The mean is u=_4.0_ girl(s). 0*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*0.102+(7-4.0)^2*0.033+(8-4.0)^2*0.005=1.957 Find sq rt of 1.957=1.4
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_.
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 different selections are possible? _____ b) What is the probability of winning? ______ c) If you win, what is your net profit? _____ d) Find the expected value. _____ e) If you bet $1.29 in a certain state's Pick 4 game, the expected value is - $0.98. Which bet is better, a $1.29 bet in the Pick 3 game or a $1.29 bet in the Pick 4 game? Explain. A) The Pick 4 game is a better bet because it has a larger expected value. B) The Pick 3 game is a better bet because it has a larger expected value. C) Neither bet is better because both games have the same expected value.
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)-$1.29(999/1000)=$-0.98
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 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 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 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 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 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 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 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 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.
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 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. x P(x) 0 0.665 1 0.277 2 0.052 3 0.005 4 0.001 5 0.000 Does the table show a probability distribution. a) Yes, the table shows a probability distribution. b) No, the random variable x's number values are not assoicated with probabilities. c) No, the random variable x is categorical instead of numerical. d) No, the sum of all probabilities is not equal to 1. e) No, not every probability is between 0 and 1 inclusive. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a) u=_____ male(s) b) The table does not show a probability distribution. Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a) o=_____ male(s) b) The table does now show a probability distribuition.
a) Yes, the table shows a probability distribution. a) u=_0.4_ male(s) 0*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. of 0.386=0.6
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 probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. Does the table show a probability distribution? Select all that apply. a) Yes, the table shows a probability distribution. b) No, the random variable x is categorical instead of numerical. c) No, the sum of all the probabilities is not equal to 1. d) No, the random variable x's number values are not associated with probabilities. e) No, not every probability is between 0 and 1 inclusive. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a) u=_____ adult(s) b) The table does not show a probability distribution. Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a) o=_____ adult(s) b) The table does not show a probability distribution.
a) Yes, the table shows a probability distribution. a) u=_0.9_ adult(s) 0*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
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 distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. x P(x) 0 0.086 1 0.339 2 0.421 3 0.154 Does the table show a probability distribution? Select all that apply. a) Yes, the table shows a probability distribution. b) No, the random variable x's number values are not assoicated with probabilites. c) No, the random variable x is categorical instead of numerical. d) No, the sume of all the probabilities is not equal to 1. e) No, not every probability is between 0 and 1 inclusive. Find the mean and random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a) u=_____ adult(s) b) The table does not show a proability distribution. Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a) o=_____ adult(s) b) The table does not show a probability variable.
a) Yes, the table shows a probability distribution. a) u=_1.6_ adult(s) 0*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
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 distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. x P(x) 0 0.029 1 0.159 2 0.312 3 0.312 4 0.159 5 0.029 Does the table show a probability distribution? Select all that apply. a) Yes, the table shows a probability distribution. b) No, not every probability is between 0 and 1 inclusive. c) No, the random variable x is categorical instead of numerical. d) No, the random variable x's number values are not associated with probabilities. e) No, the sum of all the probabilities is not equal to 1. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a) u=_____child(ren) b) The table does not show a probability distribution. Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a) o = _____ child(ren) b) The table does not show a probability distribution.
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 sq. rt. of 1.234=1.1
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 random variable.
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 runs scored during a baseball game. a) It is continuous random variable. b) It is a discrete random variable. c) It is not a random variable.
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 textbook authors now sitting at a computer. a) It is continuous random variable. b) It is a discrete random variable. c) It is not a random variable.
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 fish caught during a fishing tournament. a) It is continuous random variable. b) It is a discrete random variable. c) It is not a random variable.
b) It is discrete 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 variable.
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 political party affiliation 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 variable.
c) It is not a random variable.
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 random variable is P(x), which is the probability of a number of girls in three births. The possible values of P(x) are 0.125 and 0.375. The values of the random value P(x) are numerical. b) 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 not numerical. 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. d) The random variable is P(x), which is the probability of a number of girls in three births. The possible values of P(x) are 0.125 and 0.375. The values of the random value P(x) are not numerical.
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.
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 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. x P(x) 0 0.001 1 0.008 2 0.034 3 0.057 Does the table show a probability distribution? Select all that apply. a) Yes, the table shows a probability distribution. b) No, not every probability is between 0 and 1 inclusive. c) No, the random variable x is categorical instead of numerical. d) No, the random variable x's number values are not associated with probabilities. e) No, the sum of all probabilities is not equal to 1. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a) u=_____ women b) The table does not show a probability variable. Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a) o=_____ women b) The table does not show a probability distribution.
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.