Answer:
[tex]P(x = 5) = 0.2441[/tex]
Step-by-step explanation:
Given
[tex]p = 0.48[/tex] --- proportion that have very little confidence
[tex]n = 10[/tex] --- sample
Required
Determine the probability that exactly 5 have very little confidence
This question will be solved using binomial probability:
[tex]P(x) = ^nC_xp^x(1-p)^{n-x}[/tex]
In this case: x = 5.
So, we have:
[tex]P(x = 5) = ^{10}C_5*0.48^5(1-0.48)^{10-5}[/tex]
[tex]P(x = 5) = ^{10}C_5*0.48^5*0.52^5[/tex]
[tex]P(x = 5) = 252*0.48^5*0.52^5[/tex]
[tex]P(x = 5) = 0.2441[/tex]
