Question

(A-Grade) If 8% of all people in a certain region are unemployed, find the probability that in a sample of 200 people, there are fewer than 10 people who are unemployed. (approximate Binomial by Normal Distribution)

Answer 1

Solution:

Given that,

p = 8% = 0.08

1 - p = 1 - 0.08 = 0.92

n = 200

Here, $X\sim$ BIN (200 , 0.08)

then,

n*p = 200 * 0.08 = 16

n(1- p) = 200 * 0.92 = 184

Since both are greater than 5 , we can use normal approximation to binomial.

According to normal approximation binomial,

X $\rightarrow$ Normal

Mean = $\mu$ = n*p = 16

SD = $\sigma$ =$\sqrt{}$n*p*(1-p) = $\sqrt{}$ [200 * 0.08 * 0.92]  = 3.83666521865

P(X < 10)

= P((x - $url=https://ci3.googleusercontent.com/proxy/I4n6khLDHjbBmaHqBtVdhX-8tQKAgVc2tLy2pH2ioCCR1POUgube-VAGy3fI1uyym6NvO5meKLA81uQB=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Cmu&t=1587112289&ymreqid=f4764063-0d40-e2b0-1c62-97000101f400&sig=CnqbhL74jovXWK.I73xumw--~C$ ) / $url=https://ci3.googleusercontent.com/proxy/8pSCgvEHbaQV-QZFMeax0mpGcHmXRGWoAUJUaTzItqkuuwnZNI05S4PXM9nW20I3TJpZH3JpKWnug9x_ptAs=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Csigma&t=1587112289&ymreqid=f4764063-0d40-e2b0-1c62-97000101f400&sig=YrN5Poqs29tqL61q_FWp8w--~C$ < (10 - 16)/3.83666521865)

= P(z < -1.56)

Probability = 0.0594