Question

8.

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 0.35 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   0.275 1   0.444 2   0.239 3   0.042 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. μ= ​(Round to two decimal places as​ needed.) B. The table is not a probability distribution. Determine whether the table describes a probability distribution. If it​ does, find the mean and standard deviation. σ = ​(Round to two decimal places as​ needed.) B. The table is not a probability distribution. Is it unusual for a family of three children to consist of three​ girls?

Answer 1

Given probability distribition is,

X	P(X)	X * P(X)	X2 * P(X)
0	0.275	0	0
1	0.444	0.444	0.444
2	0.239	0.478	0.956
3	0.042	0.126	0.378
		$\sum X * P(X) = 1.048$	$\sum X^2 * P(X) = 1.778$

A) Mean of probability distribution of X is,

$\\ \mu = E(X) = \sum X * P(X) = 1.048 \\\\ => \mu = 1.05$

B) standard deviation of X is,

$\\ \sigma = \sqrt {\sum X^2 * P(X) -[E(X)]^2} = \sqrt { 1.778 - [1.048]^2 } = 0.8244 \\\\ => \sigma = 0.82$

C) Yes, P(X=3) =0.042 < 0.05 therefore, the probability of having 3 girls is unusual.