The numerical values of the mean and standard deviation are 4 and 1.55, respectively
The numerical value of the probability that x = 6.
The given parameters are:
n = 10
π = 0.4
The probability is then calculated as:
[tex]P(x) = ^nC_x * \pi^x *(1-\pi)^{n-x}[/tex]
So, we have:
[tex]P(6) = ^{10}C_6 * 0.4^6 *(1-0.4)^4[/tex]
Apply the combination formula
[tex]P(6) = \frac{10!}{6!4!} * 0.4^6 *0.6^4[/tex]
So, we have:
[tex]P(6) = 210 * 0.4^6 *0.6^4[/tex]
Evaluate
P(6) = 0.1115
Hence, the numerical value of the probability that x = 6 is 0.1115
The numerical values of the mean and standard deviation
The mean value is:
[tex]\bar x = n\pi[/tex]
This gives
[tex]\bar x = 10 * 0.4[/tex]
[tex]\bar x = 4[/tex]
The standard deviation value is:
[tex]\sigma = \sqrt{\bar x(1-\pi)[/tex]
This gives
[tex]\sigma = \sqrt{4(1-0.4)[/tex]
[tex]\sigma = 1.55[/tex]
Hence, the numerical values of the mean and standard deviation are 4 and 1.55, respectively
Read more about mean and standard deviation at:
https://brainly.com/question/16030790
#SPJ1
