Binomial random variables and the functions binompdf and binomcdf.

In this section you learned about binomial random variables and the functions binompdf and binomcdf.

An experiment is a binomial experiment if the following conditions are met:

1.            Fixed ________ _____ _______________, n.

2.            The n trials are __ are independent, which means that what happens on one trial does not influence the outcomes of other trials._____________________.

3.            There are only ______________two possible outcomes___called success and failure__________________ for each trial of the experiment.

4.            The probability, p, of a success ______doesn’t change __________________ from trial to trial.

On the bottom of page 157 is the binomial formula.  Are you ever going to use that formula in this class? _no________ (The answer in this blank is no…that’s why you have binompdf and binomcdf)

What are the two built-in functions on your calculator that we will be using to compute probabilities for binomial experiments? ______ ????(????=????)=????????????????????????????????(????,????,????)_________________ and __________ ????(????≤????)=????????????????????????????????(????,????,????)_____________

Below is the general wording for a binomial random variable:

rv X = the number of n individuals that are in some category of interest

Is this a discrete or continuous random variable? ______discrete random variable_____________

What are the possible values of this random variable? ___n and p ______________________________

Why can’t a probability be something like 2.34? _____because it is between 0 and 1

What does it mean when you get a number on your TI84 with an “E-5” after it? _it mean ______move the decimal to the right5 places____________

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

1.            a.            Given:  rv X = ___ the number of 104 randomly selected items that are defective________________________________________________

b and c:                binomial experiment with n = ___104____ and p = __0.7_____

For all parts, fill in the probability statement, write out the calculator function and values used and give an answer rounded to 4 decimal places.

d.            P(      exactly 71 are defective     ) = ______________________________________________≈ _____0.

e.            P(   less than 71 of them are defective        ) = ______________________________________________ ≈

f.             P(    more than 71 of them are defective       ) = ______________________________________________ ≈

g.            P(  exactly 73 of them are defective         ) = ______________________________________________ ≈          

h.            P(   at least 73 of them are defective        ) = ______________________________________________ ≈         

i.              P(  at most 73 of them are defective         ) = ______________________________________________ ≈

2.a.         rv X = ________ the number of 17 randomly selected people that are left-handed__________________________________________________________

                b.Givens: _n__ = ____17_____ and _p___ = ___0.12______

                c.1. There are a fixed number of people, 17

                2. There are only two outcomes for each person

                3. Whether or not one randomly selected person is left-handed will not affect whether or not another randomly selected person is left-handed

                4. p = 12% remains constant from one randomly selected person to another

                Since ______________________________ _____________, this (is/is not) a binomial experiment

d.            P(exactly none are left-handed          ) = ______________________________________________ ≈

e.            P(    exactly 14 are left-handed       ) = ______________________________________________ ≈

f.             P(  at least 9 are left-handed         ) = ______________________________________________ ≈

g.            P(  at most 12 are left-handed         ) = ______________________________________________ ≈ ____

h.            P(  at least 11 are left-handed         ) = ______________________________________________ ≈ ____0

i.              Is __11_ an unusually high value of the random variable? ___yes_ Why or why not? __________________ because P(X >= 11) <= 0.05__

If you observed __that 17 _ left-handed people in this sample, what might it tell you about the probability of a

person being left-handed? 

3.a.         rv X = ____ the number of 55 randomly selected M&Ms that are brown______________________________________________________________

b.            Givens: __n_ = _________ and _p___ = _________

c.             1. There are a fixed number of M&Ms, 55

                2. There are only two outcomes for each M&M

                3. Whether or not one randomly selected M&M is brown will not affect whether or not another randomly selected M&M is brown

                4. p = 13% remains constant from one randomly selected M&M to another

Since _________ __________________________________, this (is/is not) a binomial experiment

d.            P(   exactly none are brown        ) = ______________________________________________ ≈

e.            P(  exactly 51 are brown         ) = ______________________________________________ ≈ _________________

f.             P(  at least 47 are brown         ) = ______________________________________________ ≈ _________________

g.            P(  at most 50 are brown         ) = ______________________________________________ ≈ _________________

h.            P(  all of them are brown         ) = ______________________________________________ ≈ _________________

i.              Would it be unusual to get all brown? ______  Why or why not? _____ ________________

What might this tell you about the production process?