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