4. Probability
Basic Concepts of Probability
2:17 minutesProblem 5.q.6
Textbook Question
In Exercises 6–10, refer to the accompanying table, which describes the numbers of adults in groups of five who reported sleepwalking (based on data from “Prevalence and Comorbidity of Nocturnal Wandering In the U.S. Adult General Population,” by Ohayon et al., Neurology, Vol. 78, No. 20).
Does the table describe a probability distribution?
Verified step by step guidance1
Step 1: Understand the requirements for a probability distribution. A probability distribution must satisfy two conditions: (1) The sum of all probabilities must equal 1, and (2) each probability value must be between 0 and 1 inclusive.
Step 2: Examine the table provided. The table lists values of x (the number of adults reporting sleepwalking) and their corresponding probabilities P(x). Verify that all P(x) values are between 0 and 1.
Step 3: Add up all the probabilities in the table: P(0) + P(1) + P(2) + P(3) + P(4) + P(5). Use the values provided in the table: 0.172 + 0.363 + 0.306 + 0.129 + 0.027 + 0.002.
Step 4: Check if the sum of the probabilities equals 1. If the sum is exactly 1, the first condition for a probability distribution is satisfied.
Step 5: Confirm that all probabilities are between 0 and 1 inclusive. If both conditions are satisfied, then the table describes a probability distribution.
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