Question

Please help with this statistics problem. Will be sure to leave a review. Thank you in advance!

10. The probability that the noise level of a wide-band amplifier will exceed 2 dB is 0.15. Find the probabilities that among 9 such amplifiers the noise level of a. one will exceed 2 dB b. at most two will exceed 2 dB c. two or more will exceed 2 dB

Answer 1

p = 0.15 , n = 9

As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

a)
P(x = 1) = 9C1 * 0.15^1 * (1-0.15)^8
= 0.3679

b)

P(x <=2) = P(x =0) +P(x =1) P(x =2)
= 9C0 * 0.15^0 * (1-0.15)^9 + 9C1 * 0.15^1 * (1-0.15)^8 + 9C2 * 0.15^2 * (1-0.15)^7

= 0.8591

c) P(x >=2) = 1- P(x <=1)
= 1 - ((P(x= 0) + P(x =1))
= 1 - (9C0 * 0.15^0 * (1-0.15)^9 + 9C1 * 0.15^1 * (1-0.15)^8)
= 0.4005