Question

Let the random variable x represent the number of girls in a family with three children. Assume the probability of a child being a girl is 0.42. The table on the right describes the probability of having x number of girls. Determine whether the table describes a probability distribution. If it​ does, find the mean and standard deviation. Is it unusual for a family of three children to consist of three​ girls?

x | P(x)

0 | 0.195

1 | 0.424

2 | 0.307

3 | 0.074

Find the mean of the random variable. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. The mean is ___? (round to two decimal places as needed.

B. The table is not a probability distribution.

Find the standard deviation of the random variable. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. find the standard deviation _? (Round two decimal places as needed)

B. The table is not a probability distribution

Is it unusual for a family with three children to have only​ girls?

A. Yes, because the probability of having 3 girls is greater than 0.05.

B. No, because the probability of having 3 girls is greater than 0.05

C. Yes, because the probability of having 3 girls is less than or equal to 0.05

D. No, because the probability of having 3 girls is less than or equal to 0.05.

Answer 1

X	P(X)	X*P(X)	X² * P(X)
0	0.1950	0	0.000
1	0.4240	0.424	0.424
2	0.3070	0.614	1.2280
3	0.0740	0.222	0.6660

1) mean = E[X] = Σx*P(X) =            1.26

2)

E [ X² ] = ΣX² * P(X) =            2.3180
          
variance = E[ X² ] - (E[ X ])² =            0.7304
          
std dev = √(variance) =            0.85

3) P(X=3) = 0.0740

B. No, because the probability of having 3 girls is greater than 0.05