Question 685956: Question:
The probability of a memory chip from a production line being defective is 0.3.
i) Find the probability that, in a sample of 8 chips,there are 2 defectives.
ii) Use a suitable approximation to find the probability that, in a sample of 200 chips, there are between 55 and 65 (inclusive) defectives.
iii) A different production line had 28 deflectives in a sample of 70. Find a 95% Confidence Interval for the proportion of deflectives coming off the production line.
I have tried to solve question (i): (0.7)^6 x (0.3)^2
Thank you.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Question:
The probability of a memory chip from a production line being defective is 0.3.
----
i) Find the probability that, in a sample of 8 chips,there are 2 defectives.
Binomial Problem with n = 8 ; p(defective) = 0.3 ; p(not defective) = 0.7
P(x = 2) = 8C2(0.3)^2*(0.7)^6) = binompdf(8,0.3,2) = 0.2965
-----------------------------------
ii) Use a suitable approximation to find the probability that, in a sample of 200 chips, there are between 55 and 65 (inclusive) defectives.
P(55 <= x <= 65) = binomcdf(200,0.3,65)-binomcdf(200,0.3,54) = 0.6039
-----------------------------------------------------
iii) A different production line had 28 deflectives in a sample of 70. Find a 95% Confidence Interval for the proportion of deflectives coming off the production line.
x-bar = 28/70 = 0.4
---
E = 1.96*sqrt[0.4*0.6/70] = 0.1148
----
95% CI: 0.4-0.1148 < p < 0.4+0.1148 = (0.2852,0.5148)
==================================
Cheers,
Stan H.
|
|
|
