The probability distribution for the number of defects during an eight hour shift on the assembly line at Wanda’s Wooden Widgets is as shown in the chart below.x 0 1 2 3 4 5P(X = x) 0.50 0.25 0.15 0.06 0.03 0.01On average, how many defects are found during an 8-hour shift? 5.3 2.5 0.9 0.50 0.1667
Question
The probability distribution for the number of defects during an eight hour shift on the assembly line at Wanda’s Wooden Widgets is as shown in the chart below.x 0 1 2 3 4 5P(X = x) 0.50 0.25 0.15 0.06 0.03 0.01On average, how many defects are found during an 8-hour shift? 5.3 2.5 0.9 0.50 0.1667
Solution
To find the average number of defects found during an 8-hour shift, we need to calculate the expected value of the probability distribution. The expected value (E) is calculated by multiplying each outcome by its probability and then summing these products.
Here's how to do it:
E = (0 * 0.50) + (1 * 0.25) + (2 * 0.15) + (3 * 0.06) + (4 * 0.03) + (5 * 0.01)
E = 0 + 0.25 + 0.30 + 0.18 + 0.12 + 0.05
E = 0.90
So, on average, 0.9 defects are found during an 8-hour shift.
Similar Questions
The probability distribution for the number of defects during an 8-hour shift on the assembly line at Wanda’s Wooden Widgets is as shown in the chart below.x 0 1 2 3 4 5P(X = x) 0.50 0.25 0.15 0.06 0.03 0.01After 2 hours of a particular shift, 2 defects have already been detected. What is the probability that there will be less than a total of 4 defects detected during the entire shift? 1.00 0.96 0.84 0.25
The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution:x 0 1 2 3 4 5P(X = x) 0.20 0.30 0.20 0.15 0.10 0.05On average, how many accidents are there in the intersection in a week? 5.3 2.5 1.8 0.30 0.1667
On average, 5 % of items supplied by manufacturer X are defective. If a batch of 10 items is inspected: what is the probability that 2 items are defective 0.065 0.075 0.085 0.095
Given a normally distributed random variable X with a µ=5 and σ=2, find P(X>8).Question 4Answera.0.0001b.0.9270c.0.1862d.0.0668
The random variable X, representing the number of items sold in a week, has the following probability distribution:x 0 1 2 3 4 5 6P(X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05On average, how many items are sold in a week? 6.3 3.0 2.2 2.0 0.1428
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.