Answer:
[tex]E(x) = 4.56[/tex] --- Mean
[tex]s^2 = 1.0944[/tex] --- Variance
[tex]s = 1.0461[/tex] --- Standard Deviation
Step-by-step explanation:
See Comment for missing details
Given
[tex]p = 0.76[/tex] --- proportion
[tex]n = 6[/tex] -- sample
Solving (a): The mean; E(x)
This is calculated as:
[tex]E(x) = n * p[/tex]
Substitute values for n and p
[tex]E(x) = 6 * 0.76[/tex]
[tex]E(x) = 4.56[/tex]
Solving (b): The variance; s^2
This is calculated as:
[tex]s^2 = n*p*(1-p)[/tex]
Substitute values for n and p
[tex]s^2 = 6 * 0.76 * (1-0.76)[/tex]
[tex]s^2 = 6 * 0.76 * 0.24[/tex]
[tex]s^2 = 1.0944[/tex]
Solving (c): The standard deviation; s
This is calculated as:
[tex]s = \sqrt{s^2[/tex]
Substitute value for s^2
[tex]s = \sqrt{1.0944[/tex]
[tex]s = 1.0461[/tex]
