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**

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