Let random variable x represent the number of girls in a fam

Let random variable x represent the number of girls in a family of three children.
(a) Construct a table describing the probability distribution. (5 pts)
(b) Determine the mean and standard deviation of x. (Round the answer to two decimal places

a.

x

P(x)

0

1

2

3

Solution

Note that this is a binomial distribution, where

p = 0.5 = the probability of a girl
n = 3 trials (children)

For 0 girls:

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    3      
p = the probability of a success =    0.5      
x = the number of successes =    0      
          
Thus, the probability is          
          
P(0) =    0.125      

Similarly, we can get

P(1) = 0.375
P(2) = 0.375
P(3) = 0.125   

x   P(x)
0   0.125
1   0.375
2   0.375
3   0.125 [ANSWERS]   

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Note that

u = mean = n p = 1.5
s = sqrt[n p (1 - p)] = 0.86603 [ANSWER]