Gestation Period versus Weight The following data represent the birth weights (in grams) of babies born in 2017, along with the period of gestation.


b. What is the probability that a randomly selected baby born in 2017 weighed between 3000 and 3999 grams?

Verified step by step guidance

1. Step 1: Identify the total number of babies born in 2017 from the table. This is the grand total given in the bottom right corner of the table, which represents the sum of all babies across all birth weight categories and gestation periods.
2. Step 2: Locate the number of babies whose birth weights fall between 3000 and 3999 grams. According to the table, this is the total count in the row labeled '3000–3999' under the 'Total' column.
3. Step 3: Understand that the probability of a randomly selected baby weighing between 3000 and 3999 grams is the ratio of the number of babies in that weight category to the total number of babies born.
4. Step 4: Write the probability formula as: \(\text{Probability} = \frac{\text{Number of babies weighing 3000–3999 grams}}{\text{Total number of babies}}\)
5. Step 5: Substitute the values from the table into the formula to express the probability, but do not calculate the final value as per instructions.

Key Concepts

Probability

Probability measures the likelihood of an event occurring, expressed as a value between 0 and 1. In this context, it is the chance that a randomly selected baby’s birth weight falls within a specific range. It is calculated by dividing the number of favorable outcomes by the total number of outcomes.

Frequency Distribution

A frequency distribution organizes data into categories showing the number of observations in each. Here, birth weights are grouped into intervals with counts for different gestation periods, allowing us to sum counts within a range to find probabilities or analyze patterns.

Conditional and Marginal Totals

Marginal totals are the sums of rows or columns in a table, representing overall counts across categories. Understanding these totals helps calculate probabilities by providing the total number of observations, while conditional counts focus on specific categories, such as birth weights between 3000 and 3999 grams.