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

e. What is the probability that a randomly selected baby born in 2017 weighed less than 1000 grams and was postterm? Is this event possible?

Verified step by step guidance

1. Step 1: Understand the problem. We need to find the probability that a randomly selected baby born in 2017 weighed less than 1000 grams and was postterm. This means we are looking for the joint probability of two events: 'weight less than 1000 grams' and 'postterm gestation period'.
2. Step 2: Identify the relevant data from the table. Locate the number of babies who weighed less than 1000 grams and were postterm. According to the table, this value is 24.
3. Step 3: Identify the total number of babies born in 2017. This is given in the table as the grand total, which is 3,855,500.
4. Step 4: Calculate the probability using the formula for probability of an event: \[ P(\text{weight} < 1000 \text{ and postterm}) = \frac{\text{Number of babies with weight} < 1000 \text{ and postterm}}{\text{Total number of babies}} \] Substitute the values from the table into this formula.
5. Step 5: Consider whether this event is possible. Since the number of babies in this category is 24 (a positive number), the event is indeed possible.

Key Concepts

Probability of an Event

Probability measures the likelihood of an event occurring, calculated as the ratio of favorable outcomes to the total number of possible outcomes. In this context, it involves finding the proportion of babies with specific birth weight and gestation period relative to the total births.

Joint Probability

Joint probability refers to the chance of two events happening simultaneously, such as a baby being both postterm and weighing less than 1000 grams. It is found by dividing the count of babies meeting both criteria by the total number of babies.

Interpreting Data from Contingency Tables

Contingency tables organize data to show the frequency distribution of variables and their combinations. Understanding how to read and extract relevant counts from such tables is essential for calculating probabilities and analyzing relationships between variables.