5.1 STATISITICS HOMEWORK - RANDOM VARIABLES

he 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 0 1 2 3 ​P(x) 0.125 0.375 0.375 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. a. Find the prob. of getting exactly 6 girls in 8 births. b. Find the prob. 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. 0.106 b. 0.1141 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.

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. Use the range rule of thumb to identify a range of values that are not significant. x 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 P(x) 0.005, 0.019, 0.038, 0.115, 0.207, 0.239, 0.206, 0.113, 0.038, 0.014, 0.006

a. The maximum value in this range is ___8.4___ girls mean+2(s.d.) b. The minimum value in this range is __1.6____ girls. mean-2(s.d.) c. Based on the result, is 1 girl in 10 births a significantly low number of girls? Explain. Yes - 1 girl is a significantly low number of girls, because I girl is BELOW the range of values that are not significant.

Determine whether the value is a discrete random​ variable, continuous random​ variable, or not a random variable. a. The number of free-throw attempts before the first shot is made b. The number of fish caught during a fishing tournament c. The political party affilation of adults in the U.S. d. The amount of snowfall in December in City A e. The number of statisitcs students now reading a book f. The time required to download a file from the Internet A. Is the number of free-throw attempts before the first shot is made a discrete random​ variable, a continuous random​ variable, or not a random​ variable? B. Is the a discrete random​ variable, a continuous random​ variable, or not a random​ variable?

a. discrete b. discrete c. not a R.V. d. continuous e. discrete f. continuous

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 0 1 2 3 P(x) 0.001 0.008 0.033 0.058

a. no, the sum of all the probabilites is not equal to 1. The table does not show a probability distribution. b. The table does not show a probability distribution c. The table does not show a probability distribution

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. x 0 1 2 3 P(x) 0.366 0.428 0.182 0.024

a. yes - the table shows a probability distribution b. 0.9 adults c. 0.8 adults

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 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) 0.089 0.347 0.403 0.161

a. yes - the table shows a probability distribution b. mean = 1.6 adults c. std. dev. = 0.9 adults

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 0 1 2 3 4 5 P(x) 0.660 0.286 0.049 0.004 0.001 0.000

a. yes - the table shows a probability distribution b. mean = 0.4; st. dev. = 0.6

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

area and probability

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

continuous

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

discrete

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

expected value

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

random