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?
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