Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Normal Probability Distribution (Challenging Problem)?
Suppose a box contains 100,000 beads, of which 30,000 are black and 70,000 are red. If 10 beads are picked at a random from this box, find the probability that there are:
a) 4 black beads
b) more than 4 black beads
c) at most 6 red beads
d) no black beads
1 Answer
- paramvenuLv 71 decade agoFavorite Answer
Probability of getting a black bead = p = 30000/100000 = 3/10
q = 1-p = 1-3/10 = 7/10
n = 10
Binomial distribution is used
P(r) = nCr*q^(n-r)*p^r
a) P(r=4) = 10C4*(7/10)^6*(3/10)^4
= 210*117649/1000000*81/10000
= 0.2001
When normal approximation is used
Mean = np = 10*3/10 = 3
Standard deviation = sqrt (npq)
= sqrt (10*3/10*7/10)
= sqrt 210/100
= sqrt 2.10
= 1.45
z = (X-Mean)/S.D
a) z-score corresponding to X=4 is
z = (4-3)/1.45 = 0.69
The area under the standard normal curve corresponding to z = 0.69 is 0.2549
required probability = 0.2549
b) P(r>4) = 1 - P(r=0) - P(r=1) - P(r=2) - P(r=3)
c) P(r</=6) = 1 - P(r=7) - P(r=8) - P(r=9) - P(r=10)
d) P(r=0)
Make calculations using binomial distribution
