Please answer the full questions. 1. Refer to the accompanying table, which desc
ID: 3042881 • Letter: P
Question
Please answer the full questions.
1. Refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births.
Refer to the accompanyingtable, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births.
Number of
Girls x
P(x)
0
0.003
1
0.028
2
0.102
3
0.215
4
0.300
5
0.211
6
0.105
7
0.033
8
0.003
2.Use the magnitudes (Richter scale) of the 120 earthquakes listed in the accompanying data table. Use technology to find the range, variance, and standard deviation. If another value, 7.00, is added to those listed in the data set, do the measures of variation change much?
3.32
2.45
2.55
2.43
2.77
2.38
2.21
2.40
1.91
1.45
2.85
1.74
1.99
2.34
2.30
2.71
4.66
2.86
3.38
2.71
2.78
3.42
3.97
2.99
3.82
3.44
3.10
2.92
2.73
3.60
2.84
2.38
3.03
3.21
2.59
3.59
3.22
2.67
2.36
2.42
2.81
3.92
2.53
2.94
2.96
3.44
2.29
2.57
2.91
3.11
2.18
1.15
1.93
3.98
2.55
2.82
2.37
2.33
1.50
2.83
1.95
1.59
2.45
2.34
2.09
1.56
3.21
1.50
1.80
2.58
1.65
2.36
2.42
2.09
2.19
2.80
2.01
2.81
2.42
2.66
1.68
2.87
1.83
2.00
1.83
2.53
1.97
2.16
3.63
1.51
3.21
2.47
1.86
1.48
2.79
3.26
3.86
2.77
2.43
2.74
2.52
1.60
2.18
3.04
2.35
1.49
1.92
2.34
2.71
1.42
1.40
1.77
2.23
2.32
2.46
1.74
2.40
2.44
2.46
2.43
The mean is
U equals=
girl(s). (Round to one decimal place as needed.)
The standard deviation is
equals=nothing
girl(s). (Round to one decimal place as needed.)
Without the extra data value, the range is
.
(Type an integer or decimal rounded to three decimal places as needed.)
Without the extra data value, the standard deviation is
.
(Type an integer or decimal rounded to three decimal places as needed.)
Without the extra data value, the variance is
.
(Type an integer or decimal rounded to three decimal places as needed.)
With the extra data value, the range is
.
(Type an integer or decimal rounded to three decimal places as needed.)
With the extra data value, the standard deviation is
.
(Type an integer or decimal rounded to three decimal places as needed.)
With the extra data value, the variance is
.
(Type an integer or decimal rounded to three decimal places as needed.)
Do the measures of variation change much with the extra data value? Choose the correct answer below.
The ranges are
The variances are
And the standard deviations are
More than 5 percentage points apart,
So
all of them change
significantly.
3.The sample space listing the eight simple events that are possible when a couple has three children is {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. After identifying the sample space for a couple having four children, find the probability of getting two girls and two
boy (in any order).
Identify the sample space for a couple having four children.
{ }
(Use a comma to separate answers as needed.)
Find the probability of getting three girls and one
boy left (in any order).
nothing
(Type an integer or a decimal. Do not round.)
4. Multiple-choice questions each have
four possible answers left parenthesis a comma b comma c comma d right parenthesis(a, b, c, d),
one of which is correct. Assume that you guess the answers to three such questions.
Use the multiplication rule to find P(CWW), where C denotes a correct answer and W denotes a wrong answer
P(CWW)equals=
Refer to the accompanyingtable, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births.
Number of
Girls x
P(x)
0
0.003
1
0.028
2
0.102
3
0.215
4
0.300
5
0.211
6
0.105
7
0.033
8
0.003
Explanation / Answer
1. mean = E (X) = summation of (x*prob)
here, g = X
p= probability
g=c(0:8)
> p= c(0.003,0.028,0.102,0.215,0.300,0.211,0.105,0.033,0.003)
> mean = sum(g*p)
> mean
[1] 4.017
variance = E(X2) - E (X)2 = 1.898711
sd = sqrt (variance )
variance = sum((g^2)*p) - mean^2
> variance
[1] 1.898711
> sd= sqrt(variance)
> sd
[1] 1.377937
2.
If another value 7.00 is added then the measures of variations will change . It will increase because 7.00 is an outlier.
After adding 7.00 :
3.
Sample space = { p,q,r,s } [ where, p= b,g
q = b,g
r = b,g
s = b,g ]
Total number of events in the sample space= 2^4 = 16
Two girls and two boys can occur in 6 number of events
P [ two boys and two girls ] = 6/16 = 3/8
P[ 3 girls and 1 boy ] = 4/16 = 1/4
2 girls 2 boys :
3 girls and 1 boy:
g
Mean 2.51825 Standard Error 0.059318452 Median 2.45 Mode 2.43 Standard Deviation 0.649801085 Sample Variance 0.42224145 Kurtosis 0.331028598 Skewness 0.431463002 Range 3.51 Minimum 1.15 Maximum 4.66 Sum 302.19 Count 120