In Exercises 1–8, identify the random variable (for example, "X is the price of rutabagas"), decide whether it is continuous or discrete, and choose the most appropriate set of possible values.
A die is cast and the number that appears facing up is recorded.
The temperature is recorded at midday.
The math SAT of a random sample of college-bound students is rounded to the nearest 10 points, then recorded.
In Exercises 9–12, calculate and adjust the probability distribution histogram of the given continuous random variable by dragging the top of each bar.
Probabilities should be accurate to two decimal places.
Probability distribution histogram: To adjust the histogram drag each bar from its top edge to the appropriate height.
Farm Population, Female The following table shows the approximate number of females residing on US farms in 1990, broken down by age. Numbers are in thousands.
Source: Economic Research Service, US Department of Agriculture and Bureau of the Census, US Department of Commerce, 1990.
Farm Population, Male The following table shows the approximate number of males residing on US farms in 1990, broken down by age. Numbers are in thousands.
Figures are approximate and randomized. Source: Economic Research Service, US Department of Agriculture and Bureau of the Census, US Department of Commerce, 1990.
(a) That a large meteor hitting the earth's atmosphere will release between 1 and 4 megatons of energy.
(b) That a large meteor hitting the earth's atmosphere will release between 3 and 4.5 megatons of energy.
(c) That a large meteor will release at least 5 megatons of energy.
Meteors The following partial histogram shows part of the probability distribution of the size (in megatons of released energy) of large meteors that hit the atmosphere of planet Zor in the Cygnus III system in Andromeda.
(a) That a large meteor hitting Zor's atmosphere will release between and megatons of energy.
(b) That a large meteor hitting Zor's atmosphere will release between and megatons of energy.
(c) That a large meteor hitting Zor's atmosphere will release megatons of energy.
Quality Control An automobile parts manufacturer makes heavy-duty axles with a cross-section radius of 2.3 cm. In order for one of its axles to meet the accuracy standard demanded by the customer, the radius of the cross section cannot be off by more than 0.02 cm. Construct a probability distrbution histogram with X = the measured radius of an axle, using categories of width 0.01 cm, so that all of the following conditions are met.
(a) X is always between 2.26 and 2.34.
(b) 80% of the axles have a cross-section radius between 2.29 and 2.31.
(c) 10% of the axles are rejected.
Damage Control As a campaign manager for a presidential candidate who always seems to be getting himself into embarrassing situations, you have decided to conduct a statistical analysis of the number of times per week he makes a blunder. Construct a probability histogram with X = the number of times he blunders in a week, using categories of width 1 unit, so that all of the following conditions are met.
(a) X is always between and (inclusive).
(b) During a given week, there is an 80% chance that he will make to blunders.
(c) Never a week goes by when he doesn't make at least blunders.
(d) On occasion, he has made blunders in one week.
How is a random variable related to the outcomes in an experiment?
Give an example of an experiment and two associated continuous random variables.
You are given a probability distribution histogram with the bars having a width of 2 units. How is the probability P(a \leq X \leq b) related to the area of the corresponding portion of the histogram?
You are given a probability distribution histogram with the bars having a width of 1 unit, and you wish to convert it into one with bars of width 2 units. How would you go about this?