Chapter 5.1 HW

...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. 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. .112 B. .124 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 light bulbs that burn out in the next week in a room with 11 bulbs b. The square footage of a house c. The political party affiliation of adults in the United States d. The exact time it takes to evaluate 27+72 e. The number of textbook authors now sitting at a computer f. The time required to download a file from the internet

A. it is discrete random variable B. continuous random variable C. not random variable D. continuous random variable E. discrete random variable F. continuous random variable

In a​ state's lottery, you can bet ​$1 by selecting three​ digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same​ order, you win and collect ​$500. 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 for a ​$1 bet. e. If you bet $1 on a certain casino​ game, the expected value is −1.7​¢. Which bet is better in the sense of producing a higher expected​ value: a $1 bet on the​ state's lottery or a $1 bet on the casino​ game? Explain.

A. 1000 B. .001 (1/1000) C. $499 D. -.5 (.001)(499)-(-1)(.999) E. The casino game is a better bet because it has a larger expected value.

The accompanying table describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition​ allowed, and the random variable x is the number of digits that match those in the same order that they are drawn​ (for a​ "straight" bet). Use the range rule of thumb to determine whether 4 matches is a significantly high number of matches. X 0 1 2 3 4 P(X) .662 .291 .042 .006 0+ Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice

Significantly high numbers of matches are 1.6 or more. Since 4 is at least as high as this​ value, 4 matches is a significantly high number of matches mean + 2* standard deviation

The accompanying table lists probabilities for the corresponding numbers of unlicensed software packages. What is the random​ variable, what are its possible​ values, and are its values​ numerical? # unlicensed software packages 0 1 2 3 P(x) .125 .375 .375 .125

The random variable is​ x, which is the number of unlicensed software packages. The possible values of x are​ 0, 1,​ 2, and 3. The values of the random value x are numerical.

A​ _______ random variable has either a finite or a countable number of values.

discrete

College students are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they take one or more online courses. 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 0 1 2 3 p(x) .104 .351 .397 .148 Does the table show a probability​ distribution? Select all that apply.

Yes, the table shows a probability distribution. 1.6 =mean (.351*1)+(.397*2)+(.148*3) .9 = standard deviation squrt ( (sum of X^2 * p(x) ) - (mean ^2) )

In a probability​ histogram, there is a correspondence between​ _______.

area and probability

A​ _______ random variable has infinitely many values associated with measurements.

continuous

The​ _______ of a discrete random variable represents the mean value of the outcomes.

expected value

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 0.175 1 0.357 2 0.312 3 0.126 4 0.026 5 .004

mean = 1.5 standard deviation = 1.0

A​ _______ variable is a variable that has a single numerical​ value, determined by​ chance, for each outcome of a procedure.

random

​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

In a​ survey, cell phone users were asked which ear they use to hear their cell​ phone, and the table is based on their responses. 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. Left Right No Preference P(X) .636 .304 .060 Does the table show a probability?

​No, the random variable x is categorical instead of numerical. The table does not show a probability distribution. The table does not show a probability distribution.

Households are randomly selected and partitioned into groups of four. For those​ groups, the random variable x is the number of households with a printer. 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 0 1 2 3 4 P(X) .026 .147 .331 .358 .138

​Yes, the table shows a probability distribution. mean = 2.4 (0*.026)+(1*.147)*(2*.331)+(3*.358)+(4*.138) standard deviation = 1 squrt ( (sum of X^2 * p(x) ) - (mean ^2) )