Harper MTH165 Homework Section 5.3 Latest 2020 MAY

MTH165 ELEMENTARY STATISTICS

Homework Section 5.3

In this section you learned how to compute the mean and standard deviation for a binomial random variable.

Fill in the formulas for the mean and standard deviation of a binomial random variable:

For a binomial distribution:  ______________________ and ______________________

You can draw the binomial histograms using StatCrunch.  Use ___Stat____, Calculators___________, ______.  Fill in the value of n & p from the problem and then enter P( _________ ) before you click “Compute”

                What are the 4 shapes that we discussed for histograms back on page 43?

__________________, __________________, _________________, ______________

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

1.            Given:  binomial experiment with n = __6_____ and p = _0.12______

                a.            (Your version might not use all of the cells displayed below)

X             0              1              2              3              4              5              6             

P(X)       0.464     0.380     0.130     0.024     0.002     0.000     0.000    

                b.            Make a quick sketch (takes just a few seconds) of the correct histogram.

                c.             Which of the 4 shapes discussed in this class does this histogram most resemble?

d.                                            _____ = _______________ = ____________ = _________________

Symbol                 formula with symbols                    formula with numbers                                   number                                                units

                e.            __ ___ = _________ _______________ = _____  _____________                    

Symbol                 formula with symbols                    formula with numbers                                                   number                                                units

2              Given:  binomial experiment with n = ____6___ and p = __0.84_____

                a.            (Your version might not use all of the cells displayed below)

X             0              1              2              3              4              5              6             

P(X)       0.000     0.001     0.007     0.049     0.191     0.401     0.351    

b.            Make a quick sketch (takes just a few seconds) of the correct histogram.

c.             Which of the 4 shapes discussed in this class does this histogram most resemble? ________________

d.            __ ___ = __________________ = ___________________ = _________  _____________                    Symbol                 formula with symbols                    formula with numbers                                                   number                                                units     

e.            = ____________ = = _________  _____________

Symbol                 formula with symbols    formula with numbers                                                   number                                                units

3.            Given:  binomial experiment with n = _______ and p = _______

                a.            (Your version might not use all of the cells displayed below)

X             0              1              2              3              4              5              6             

P(X)       0.016     0.094     0.234     0.313     0.234     0.094     0.016    

b.            Make a quick sketch (takes just a few seconds) of the correct histogram.

c.             Which of the 4 shapes discussed in this class does this histogram most resemble? ___Bell shaped_______________

__  ___ = __________________ = ___________________ = _________  _____________

Symbol                 formula with symbols                    formula with numbers                                                   number                                                units

                                ___ σ___ = = = ____1____  _____________

Symbol                 formula with symbols                    formula with numbers                                                   number                                                units

4.In problem 1, p __<__ 0.5 and the shape of the probability histogram was __ ___________________

In problem 2, p __>__ 0.5 and the shape of the probability histogram was ___ __________________

In problem 3, p _=___ 0.5 and the shape of the probability histogram was _ ____________________

This relation is not just true for these binomial histograms.  This is true for all binomial histograms.

5.a.         rv X = ____________the number of 26 randomly selected people that are

b.            Given:  binomial experiment with n = _____ and p = ______

c.             __ ___ = _________________ = __________________ = ___2______  _____________

Symbol                 formula with symbols                    formula with numbers                   number                                                unit

Interpret the mean in the context of this problem:  _ Out of every 26 people, 2.86 of them on average are left-handed

d.            σ = _______________ = ___= _________  _____________

Symbol                 formula with symbols    formula with numbers                   number                                                units

6.a.         rv X = _______ the number of 49 randomly selected M&Ms that are brown _________________________________________________________________

b.            Given:  binomial experiment with n = _______ and p = ______

c.             ____  ___ = __________________ = ___________________ = _________  _____________

Symbol                 formula with symbols    formula with numbers   number                                units

Interpret the mean in the context of this problem:  __Out of every 49 M&Ms, 6.86 of them on average are brown

d.            __  ___ = __________________ = _____________ = ________  _____________

Symbol                 formula with symbols                    formula with numbers                   number                                                units