Question

A drawer contains black socks and white socks. 40% of the socks are black socks. A number generator simulates randomly selecting 10 socks from the drawer. The number generator is used 10 times and the number of black socks in each trial is shown in the dot plot.
Which description is correct about the number generator being fair or not?




a)The number generator is not fair. It picked black socks half of the time.

b)The number generator is not fair. In three experiments, it picked black socks 50% of the time.

c)The number generator is fair. It picked the approximate percentage of black socks most of the time.

d)The number generator is fair. It picked black socks half of the time.

Answer 1

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.