Question

Use

nequals=66

and

pequals=0.60.6

to complete parts​ (a) through​ (d) below.

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

x	​P(x)
0	nothing
1	nothing
2	nothing
3	nothing
4	nothing
5	nothing
6	nothing

​(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 XμXequals=nothing

​(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 XμXequals=nothing

​(Round to two decimal places as​ needed.)

sigma Subscript Upper XσXequals=nothing

​(Round to two decimal places as​ needed.)

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

sigma Subscript Upper XσXequals=nothing

​(Round to two decimal places as​ needed.)

A.

03600.250.5xP(x)

A graph with a horizontal x-axis labeled from 0 to 6 in intervals of 1 and a vertical y-axis labeled from 0 to 0.5 in intervals of 0.05 has seven vertical line segments, one for each horizontal axis label. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the approximate line segment height listed second: 0, 0.00; 1, 0.04; 2, 0.14; 3, 0.28; 4, 0.31; 5, 0.19; 6, 0.05.

B.

03600.250.5xP(x)

A graph with a horizontal x-axis labeled from 0 to 6 in intervals of 1 and a vertical y-axis labeled from 0 to 0.5 in intervals of 0.05 has seven vertical line segments, one for each horizontal axis label. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the approximate line segment height listed second: 0, 0.28; 1, 0.31; 2, 0.19; 3, 0.05; 4, 0.19; 5, 0.31; 6, 0.28.

C.

03600.250.5xP(x)

A graph with a horizontal x-axis labeled from 0 to 6 in intervals of 1 and a vertical y-axis labeled from 0 to 0.5 in intervals of 0.05 has seven vertical line segments, one for each horizontal axis label. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the approximate line segment height listed second: 0, 0.31; 1, 0.28; 2, 0.14; 3, 0.14; 4, 0.14; 5, 0.28; 6, 0.31.

D.

03600.250.5xP(x)

A graph with a horizontal x-axis labeled from 0 to 6 in intervals of 1 and a vertical y-axis labeled from 0 to 0.5 in intervals of 0.05 has seven vertical line segments, one for each horizontal axis label. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the approximate line segment height listed second: 0, 0.00; 1, 0.04; 2, 0.14; 3, 0.28; 4, 0.31; 5, 0.28; 6, 0.14.The binomial probability distribution is

▼

symmetric.

skewed right.

bimodal.

skewed left.

Answer 1

a)

x	f(x)
0	0.0041
1	0.0369
2	0.1382
3	0.2765
4	0.3110
5	0.1866
6	0.0467

b)

E(x) =μ=	ΣxP(x) =	3.6000
E(x2) =	Σx2P(x) =	14.4000
Var(x)=σ2 =	E(x2)-(E(x))2=	1.4400
std deviation=	σ= √σ2 =	1.2000

from above μx=3.6

σx =1.20

c)_

μx=np=6*0.6=3.6

σx =sqrt(np(1-p))=1.20

d)

skewed left