Respuesta :
Answer:
The binomial probability distribution is shown below.
Step-by-step explanation:
The probability mass function of X is:
[tex]P(X=x)={n\choose x}p^{x}(1-p)^{n-x};x=0,1,2,3..[/tex]
It is provided that n = 6 and p = 0.25.
Construct a binomial probability distribution with the given parameters as follows:
X P (X = x)
0 [tex]P(X=0)={6\choose 0}(0.25)^{0}(1-0.25)^{6-0}= 0.1780[/tex]
1 [tex]P(X=1)={6\choose 1}(0.25)^{1}(1-0.25)^{6-1}= 0.3560[/tex]
2 [tex]P(X=2)={6\choose 2}(0.25)^{2}(1-0.25)^{6-2}= 0.2966[/tex]
3 [tex]P(X=3)={6\choose 3}(0.25)^{3}(1-0.25)^{6-3}= 0.1318[/tex]
4 [tex]P(X=4)={6\choose 4}(0.25)^{4}(1-0.25)^{6-4}= 0.0330[/tex]
5 [tex]P(X=5)={6\choose 5}(0.25)^{5}(1-0.25)^{6-5}= 0.0044[/tex]
6 [tex]P(X=6)={6\choose 6}(0.25)^{6}(1-0.25)^{6-6}= 0.0002[/tex]
Compute the mean and standard deviation as follows:
[tex]\mu=np=6\times0.25=1.50\\\\\sigma=\sqrt{np(1-p)}=\sqrt{6\times 0.25\times (1-0.25)}=1.0607[/tex]
Binomial probability distribution was constructed, and the mean and standard deviation comes to be 1.5 and 1.061 respectively.
As we know that binomial probability distribution is given by
[tex]P(x) = ^nC_xp^x(1-p)^{n-x}[/tex]
What is binomial distribution?
The binomial distribution is a probability distribution that depicts the likelihood that a value will take one of two independent values under a given set of parameters.
Given n=6 & p=0.25
[tex]P(0) = ^6C_0(0.25)^0(1-0.25)^{6-0}[/tex] = 0.1780
[tex]P(1) = ^6C_1(0.25)^1(1-0.25)^{6-1}[/tex]=0.3560
[tex]P(2) = ^6C_2(0.25)^2(1-0.25)^{6-2}[/tex] = 0.2966
[tex]P(0) = ^6C_3(0.25)^3(1-0.25)^{6-3}[/tex] =0.1318
[tex]P(0) = ^6C_4(0.25)^4(1-0.25)^{6-4}[/tex]=0.0330
[tex]P(5) = ^6C_5(0.25)^5(1-0.25)^{6-5}[/tex]=0.0044
[tex]P(6) = ^6C_6(0.25)^6(1-0.25)^{6-6}[/tex]= 0.0002
Mean = np
Mean = 6*0.25
Mean = 1.5
Standard deviation σ = [tex]\sqrt{np(1-p)}[/tex]
σ = [tex]\sqrt{6*0.25(1-0.25)}[/tex]
σ = 1.061
Hence, binomial probability distribution was constructed, and the mean and standard deviation comes to be 1.5 and 1.061 respectively.
To get more about binomial distribution visit:
https://brainly.com/question/24756209
