Use n=6 and p=0.8 to complete parts (a) through (d) below.

(a) Construct a binomial probability distribution with the given parameters.

x

P(x)

0



1



2



3



4



5



6



(Round to four decimal places as needed.)

(b) Compute the mean and standard deviation of the random variable using

mu Subscript Upper XμXequals=Summation from nothing to nothing left bracket x times Upper P left parenthesis x right parenthesis right bracket∑[x•P(x)]

and

sigma Subscript Upper XσXequals=StartRoot Summation from nothing to nothing left bracket x squared times Upper P left parenthesis x right parenthesis right bracket minus mu Subscript Upper X Superscript 2 EndRoot∑x2•P(x)−μ2X.

mu Subscript Upper X μX=

(Round to two decimal places as needed.)

sigma Subscript Upper X σX=

(Round to two decimal places as needed.)

(c) Compute the mean and standard deviation, using

mu Subscript Upper XμXequals=np

and

sigma Subscript Upper XσXequals=StartRoot np left parenthesis 1 minus p right parenthesis EndRootnp(1−p).

mu Subscript Upper X μX=

(Round to two decimal places as needed.)

sigma Subscript Upper X σX=

(Round to two decimal places as needed.)

(d) Draw a graph of the probability distribution and comment on its shape.