Answer:
c)The number generator is fair. It picked the approximate percentage of black socks most of the time.
Step-by-step explanation:
given that 40% are black socks.
No of socks that can be black can take values as
X =0,1,2....10
Each sock is independent of the other.
Hence X is binomial with n = 10 , p = 0.4 and q = 0.6
P(x=r) = 10Cr (0.4)^r (0.6)^(10-r)
r = 0,1,2...10
P(X=0) = 0.0060
P(X=1) = 0.0403
P(X=2) = 0.1209
x 0 1 2 3 4 5 6
Prob 0.0060 0.0403 0.1209 0.2150 0.2508 0.2007 0.1115
7 8 9 10
0.0425 0.0106 0.0016 0.0001
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Comparing with the dot plot we find that the probability increases upto 4 attains peak and comes down and almost negligible for 0,1,9 and 10.
But for 6, 7, 8 prob is not 0 but approximately dot plot is consistent with the theoretical results.
c)The number generator is fair. It picked the approximate percentage of black socks most of the time.