Answer:
0.118 ; (271, 329)
Step-by-step explanation:
Given;
Probability of success , p = 0.3
Number of trials, n = 12
P(x ≥ 6) = P(6) + P(7) + P(8) + P(9) + P(10)
Using binomial probability formula :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
Using calculator :
P(x ≥ 6) = 0.1178
= 0.118
B.)
Suppose number of trials, n = 1000
And number of defective chickens is within 1 standard deviation of the mean :
Mean = np ; p = 0.3
Mean = 1000 * 0.3 = 300
Standard deviation (s) : sqrt(np(1-p))
s = sqrt(1000 * 0.3 * 0.7)
s = sqrt(210)
s = 14.49
2 standard deviations of the mean:
Mean ± 2s
Lower bound : 300 - 2(14.49) = 271.02
Upper bound : 300 + 2(14.49) = 328.98
(271.02, 328.98) = (271, 329)
