Section 5.1 Homework
A _______ random variable has either a finite or a countable number of values.
Discrete
A _______ variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.
Random
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. x P(x) 0 0.004 1 0.019 2 0.037 3 0.114 4 0.198 5 0.234 6 0.204 7 0.113 8 0.039 9 0.013 10 0.025
The maximum value in this range is 8.7 girls. The minimum value in this range is 1.5 girls. Yes, 1 girl is a significantly low number of girls, because 1 girl is below the range of values that are not significant.
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 0.176 1 0.362 2 0.301 3 0.129 4 0.028 5 0.004
The mean is 1.5 sleepwalker(s). The standard deviation is 1.0 sleepwalker(s).
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 P(x) 0 0.125 1 0.375 2 0.375 3 0.125
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.
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. Number of Girls x P(x) 0 0.005 1 0.009 2 0.119 3 0.226 4 0.282 5 0.226 6 0.119 7 0.009 8 0.005 a. Find the probability of getting exactly 1 girl in 8 births. b. Find the probability of getting 1 or fewer girls in 8 births. c. Which probability is relevant for determining whether 1 is a significantly low number of girls in 8 births: the result from part (a) or part (b)? d. Is 1 a significantly low number of girls in 8 births? Why or why not? Use 0.05 as the threshold for a significant event.
a. 0.009 b. 0.014 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 the random variable x, the numbers of adults in groups of five who reported sleepwalking. Complete parts (a) through (d) below. x P(x) 0 0.188 1 0.341 2 0.296 3 0.135 4 0.031 5 0.009 a. Find the probability of getting exactly 4 sleepwalkers among 5 adults. b. Find the probability of getting 4 or more sleepwalkers among 5 adults. c. Which probability is relevant for determining whether 4 is a significantly high number of sleepwalkers among 5 adults: the result from part (a) or part (b)? d. 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. 0.031 b. 0.04 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.
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. Number of Girls x P(x) 0 0.002 1 0.007 2 0.112 3 0.208 4 0.342 5 0.208 6 0.112 7 0.007 8 0.002 a. Find the probability of getting exactly 6 girls in 8 births. b. Find the probability of getting 6 or more girls in 8 births. c. 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)? d. Is 6 a significantly high number of girls in 8 births? Why or why not? Use 0.05 as the threshold for a significant event.
a. 0.112 b. 0.121 c. The result from part b, since it is the probability of the given or more extreme result. d. No, since the appropriate probability is greater than 0.05, it is not a significantly high number.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of bald eagles in a country b. The number of light bulbs that burn out in the next week in a room with 12 bulbs c. The gender of college students gender of college students d. The number of statistics students now reading a book e. The number of textbook authors now sitting at a computer f. The number of points scored during a basketball game
a. It is a discrete random variable b. discrete random variable c. It is not a random variable d. discrete random variable e. discrete random variable f. discrete random variable
Determine whether the following value is a continuous random variable, discrete random variable, or not a random variable. a. The number of free dash throw attempts before the first shot is missed b. The usual mode of transportation of people in City Upper A c. The number of hits to a website in a week d. The time required to upload a file to the Internet e. The weight of a hamburger f. The number of home runs in a baseball game
a. discrete random variable b. It is not a random variable c. discrete random variable d. continuous random variable e. continuous random variable f. discrete random variable
In a probability histogram, there is a correspondence between _______.
area and probability
A _______ random variable has infinitely many values associated with measurements.
continuous
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of statistics students now reading a book b. The number of textbook authors now sitting at a computer c. The gender of college students d. The number of people with blood type Upper A in a random sample of 18 people e. The height of a randomly selected giraffe f. The time it takes for a light bulb to burn out
discrete random variable b. discrete random variable c. not a random variable. d. discrete random variable e. continuous random variable f. continuous random variable
The _______ of a discrete random variable represents the mean value of the outcomes.
expected
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. x P(x) 0 0.006 1 0.011 2 0.043 3 0.113 4 0.198 5 0.247 6 0.196 7 0.114 8 0.042 9 0.018 10 0.012
maximum value range= 8.5 minimum value in this range= 1.6 Yes, 1 girl is a significantly low number of girls, because 1 girl is below the range of values that are not significant.
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 births. Number of Girls x P(x) 0 0.003 1 0.029 2 0.109 3 0.224 4 0.266 5 0.221 6 0.108 7 0.035 8 0.005
μ= 4.0 σ= 1.4
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
No, the sum of all the probabilities is not equal to 1. b. The table does not show a probability distribution. c. The table does not show a probability distribution.
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 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 0.654 1 0.287 2 0.053 3 0.005 4 0.001 5 0.000
Yes, the table shows a probability distribution. b. μ= 0.4 c. σ= 0.6
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 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 0.034 1 0.149 2 0.317 3 0.317 4 0.149 5 0.034
Yes, the table shows a probability distribution. b. μ= 2.5 child(ren) c. σ= 1.1 child(ren)