Logan wants to know how many skateboards have defective parts. He inspects skateboards and keeps track of the number of defects per board. Use his probability distribution table to find the expected value for defects on a skateboard.
To find the expected value for defects on a skateboard using Logan's probability distribution table, you need to perform a simple calculation.
First, let's understand the probability distribution table. It consists of two columns: "Number of Defects" and "Probability." The "Number of Defects" column represents the possible number of defects on a skateboard, while the "Probability" column represents the likelihood (probability) of each number of defects occurring.
To calculate the expected value, you multiply each number of defects by its corresponding probability and then sum them all up.
Here's the step-by-step process using Logan's probability distribution table:
1. Multiply each number of defects by its corresponding probability.
- For example, if the table shows the number of defects as 0, 1, 2, and their probabilities as 0.4, 0.3, and 0.3, respectively:
- Multiply 0 (number of defects) by 0.4 (probability): 0 x 0.4 = 0
- Multiply 1 (number of defects) by 0.3 (probability): 1 x 0.3 = 0.3
- Multiply 2 (number of defects) by 0.3 (probability): 2 x 0.3 = 0.6
2. Sum all the products calculated in step 1.
- In this example, add up the three calculated values: 0 + 0.3 + 0.6 = 0.9
3. The resulting value from step 2 is the expected value for defects on a skateboard.
- In this example, the expected value is 0.9.
So, Logan can expect an average of 0.9 defects on a skateboard based on the given probability distribution table.