Answer:
P(X ≥ 5) = 0.99972
Step-by-step explanation:
From the given data;
[tex]X \sim B(n = 2000 ;p = 0.01)[/tex]
Mean [tex]\mu = np[/tex]
Mean [tex]\mu = 2000 \times 0.01[/tex]
Mean [tex]\mu = 20[/tex]
Standard deviation [tex]\sigma = \sqrt{np (1-p)}[/tex]
[tex]\sigma = \sqrt{2000 \times 0.01 (1-0.01)}[/tex]
[tex]\sigma = \sqrt{20(0.99)}[/tex]
[tex]\sigma = \sqrt{19.8}[/tex]
[tex]\sigma =[/tex] 4.44972
P(X ≥ 5) ; The discrete distribution by continuous normal distribution for P(X ≥ 5) lies between 4.5 and 5.5. Hence, Normal distribution x = 4.5 since greater than or equal to is 5 relates to it.
Now;
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]
[tex]z = \dfrac{4.5 - 20}{4.4972}[/tex]
[tex]z = \dfrac{-15.5}{4.4972}[/tex]
z = −3.45
P(X > 4.5) = P(Z > -3.45)
P(X > 4.5) = 1 - P (Z < - 3.45)
From Normal Z tables;
P(X > 4.5) = 1 - 0.00028
P(X > 4.5) = 0.99972
P(X ≥ 5) = 0.99972
