The following data represent the number of live...

The following data represent the number of live multiple-delivery births (three or more babies) in 2012 for women 15 to 54 years old. $$ \begin{array}{lc} \text { Age } & \text { Number of Multiple Births } \\ \hline 15-19 & 44 \\ \hline 20-24 & 404 \\ \hline 25-29 & 1204 \\ \hline 30-34 & 1872 \\ \hline 35-39 & 1000 \\ \hline 40-44 & 332 \\ \hline 45-54 & 63 \end{array} $$ (a) Construct a probability model for number of multiple births. (b) In the sample space of all multiple births, are multiple births for 15 - to 19 -year-old mothers unusual? (c) In the sample space of all multiple births, are multiple births for 40 - to 44 -year-old mothers unusual?

The following data represent the number of live multiple-delivery births (three or more babies) in 2012 for women 15 to 54 years old.
$$
\begin{array}{lc}
\text { Age } & \text { Number of Multiple Births } \\
\hline 15-19 & 44 \\
\hline 20-24 & 404 \\
\hline 25-29 & 1204 \\
\hline 30-34 & 1872 \\
\hline 35-39 & 1000 \\
\hline 40-44 & 332 \\
\hline 45-54 & 63
\end{array}
$$
(a) Construct a probability model for number of multiple births.
(b) In the sample space of all multiple births, are multiple births for 15 - to 19 -year-old mothers unusual?
(c) In the sample space of all multiple births, are multiple births for 40 - to 44 -year-old mothers unusual?

Key Concepts

Unusual Event

An unusual event in a probability model is typically one with a very low probability, often determined by a threshold such as 5% (or 0.05). This concept helps in identifying outcomes that rarely occur under normal circumstances by evaluating whether their probability lies in the tail of the distribution.

Sample Space

The sample space is the set of all possible outcomes in an experiment or process. In the context of a probability distribution, it encompasses every possible category or event for which probabilities are defined. Understanding the sample space is essential for correctly interpreting the probability model and assessing whether specific events, such as those that might be considered unusual, occur frequently or rarely.

Probability Distribution

A probability distribution provides a mapping from outcomes to their probabilities. In topics like these, a frequency table is transformed into a probability model by dividing each frequency by the total number of cases. This process results in a probability distribution that fully describes how probabilities are assigned to different outcomes, ensuring that the sum of all probabilities equals 1.

Relative Frequency

Relative frequency is the ratio of the frequency of an event to the total frequency of all events. It is used to estimate probabilities in empirical data. By calculating relative frequencies from observed data, one can infer the probability of each outcome occurring, which is the foundation of constructing a probability model.

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