

Applied calculus exercises: continuous random variables and histograms 
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.
A die is cast and
A dial is spun, and the angle (measured clockwise) the pointer makes with the vertical is noted. (See the figure.)
A dial of radius one unit is spun (see the figure above), and
The temperature is recorded at midday.
The math SAT of a random sample of collegebound 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.
Frequency distribution:
\pmb{X} = Height of a jet fighter (thousand feet)  
Number 
Probability distribution histogram: To adjust the histogram drag each bar from its top edge to the appropriate height.

Frequency distribution:
\pmb{X} = Time between eruptions of local volcano (thousand years)  
Frequency 
Probability distribution histogram: To adjust the histogram drag each bar from its top edge to the appropriate height.

Frequency distribution:
\pmb{X} = Average temperature (°F)  
Number of Cities 
Probability distribution histogram: To adjust the histogram drag each bar from its top edge to the appropriate height.

Frequency distribution:
\pmb{X} = Cost of a used car ($1000)  
Number of cars 
Probability distribution histogram: To adjust the histogram drag each bar from its top edge to the appropriate height.

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 earth's atmosphere. (A large meteor is one that releases at least one megaton of energy, equivalent to the energy released by a small nuclear bomb.)
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.
Quality Control An automobile parts manufacturer makes heavyduty axles with a crosssection 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.
Probability distribution histogram: To adjust the histogram drag each bar from its top edge to the appropriate height.
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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.
Probability distribution histogram: To adjust the histogram drag each bar from its top edge to the appropriate height.
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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?