Probabilities for continuous random variables correspond to area under a probability distribution curve over a particular interval.

In this section you learned how probabilities for continuous random variables correspond to area under a probability distribution curve over a particular interval.

We start this chapter with the uniform distribution because the area under a uniform distribution curve will always be in the shape of a rectangle and the formula for the area of a rectangle is ________.

For a continuous random variable, whether or not the endpoints are included in the interval will not change _________________________________________.

That means for a continuous random variable, P(5<X<10) ?(?(<@>@=))   P(5≤X≤10)

(Pick the correct symbol from the 3 choices in the box)

                For a continuous random variable, P(X = a number) will ALWAYS be _____.

                That means, if X = the weight of a newborn baby, then P(X = 7 pounds) = _____

                That means, if X = the temperature at a particular time, then P(X = 32 degrees) = ____

                That means, if X = the driving speed of a car, then P(X = 70 mph) = _____

Fill in the following as you work through your given problems in MyOpenMath.

1.            Given:  Uniform distribution over the interval from ____ to ____

                a.            rv X = ________________ the time it takes me to wash dishes on a randomly selected night

                b.            Compute the height of this uniform distribution:  height = __________

                c.             Draw a picture of the distribution like we did in the examples in the book. 

Clearly label the horizontal axis and designate the height of the curve.

a rectangle with edges at 7 and 17

                d.            Fill in the probability statement, your computation and final answer. 

                                Include a sketch of the corresponding area like was done in all parts of Example #6.1.1.

                                P(     between 10 and 16 minutes             ) = _________________________ ≈ _________

                                Interpret in the context of this problem:

                                Would the probability on this one be any different if the endpoints were included in the interval? __                                     Why not? ____because ????(????≤????≤????)=????(????<????<????)____________________________________________________________

                e.            P(      exactly 10 minutes            ) = ____________

2.            Given:  Uniform distribution over the interval from __ to ____

                a.            rv X = ______ the waiting time for a randomly selected commuter on the Red Line during peak rush hours ______________________________________________________

                b.            Compute the height of this uniform distribution:  height = __________

                c.             Draw a picture of the distribution like we did in the examples in the book. 

Clearly label the horizontal axis and designate the height of the curve.

 a rectangle with edges at 0 and 13

                d.            Fill in the probability statement, your computation and final answer. 

                                Include a sketch of the corresponding area like was done in all parts of Example #6.1.1.

                                P(     between 4 and 7              ) = __________________________ ≈ __________

                                Interpret in the context of this problem:

                                Would the probability on this one be any different if the endpoints were included in the interval? __                                     Why not? __________ ????(????≤????≤????)=????(????<????<????)___________________________________________________

                e.            P(    exactly 4              ) = ____________

It will extremely important in the rest of the course that you know all of the inequality symbols and the typical wording we see for each of them.  Fill in the following table with the correct inequality symbol (which means don’t guess….look them up):

is at least             >=                           is greater than or equal to            >=

is at most             <=                           is less than or equal to   <=

is less than          <                             exceeds               >

is greater than   >                             does not exceed              <=

is a maximum of               <=                           is below               <

is a minimum of                >=                           is above               >

is no less than    >=                           is no greater than            <=

is between         <      <                     is between inclusive       <=   <=

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