Harper MTH165 Homework Section 5.2 Latest 2020 MAY

MTH165 ELEMENTARY STATISTICS

Homework Section 5.2

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?