Respuesta :
Answer:
Probability = 0.894
Expected value = 5.2
Standard deviation = 1.349
Step-by-step explanation:
Given that
p = 0.65
n = 8
q = 1 - p
= 1 - 0.65
= 0.35
[tex]P(x) = ^n(c_x)\times P^x\times q^{n-x}[/tex]
For P(3)
[tex]= ^8c_3\times 0.65^3\times 0.35^5[/tex]
Which gives result
= 0.0808
For P(2)
[tex]= ^8c_2\times 0.65^2\times 0.35^6[/tex]
Which gives result
= 0.0217
For P(1)
[tex]= ^8c_1\times 0.65^1\times 0.35^7[/tex]
which gives result
= 0.0033
For P(0)
[tex]= 0.35^8[/tex]
= 0.0002
Now probability is at least getting admitted of 4 students
= 1 - {P(3) + P(2) + P(1) + P(0)}
= 1 - (0.0808 + 0.0217 + + 0.0033 + 0.0002)
= 1 - 0.106
= 0.894
Expected value = [tex]n\times p[/tex]
[tex]= 8\times 0.65[/tex]
= 5.2
Standard deviation
[tex]= \sqrt{n\times p\times q} \\\\\ = \sqrt{8\times 0.65\times 0.35}[/tex]
= 1.349
