A vacuum cleaner company has three machines, each making electric cords.
Machine 1 is the oldest and of all units it produces 1.2% do not meet quality standard (of not being damaged after an abrupt change of voltage). Machine 2 produces 0.8% of bad units, while the newest, machine 3, makes 0.5% of units with unacceptable quality. Of all the cords produced, 20% are made on machine 1, 35% are made on machine 2 and the rest on the machine 3. The cord is used as a part of vacuum cleaner that the company makes. If a customer randomly buys a vacuum cleaner produced by this company, what is the probability that the cord does
not meet the quality standard?
0.936%
Well, let's clown around with some numbers, shall we?
First, let's calculate the overall probability of a cord not meeting the quality standard. We'll multiply the probability of each machine producing a bad unit by the percentage of cords produced by that machine.
So, for machine 1, the probability of a bad unit is 1.2% (or 0.012) and the percentage of cords produced is 20% (or 0.2). So, the contribution of machine 1 to the overall probability is 0.012 * 0.2 = 0.0024.
Similarly, for machine 2, the probability of a bad unit is 0.8% (or 0.008) and the percentage of cords produced is 35% (or 0.35). So, the contribution of machine 2 to the overall probability is 0.008 * 0.35 = 0.0028.
Now, for machine 3, the probability of a bad unit is 0.5% (or 0.005). Since the remaining cords are made on machine 3, which is 45% (since 20% + 35% = 55%, and the remaining percentage from 100% is 45%), the contribution of machine 3 to the overall probability is 0.005 * 0.45 = 0.00225.
Finally, summing up the contributions from each machine, the overall probability of a cord not meeting the quality standard would be 0.0024 + 0.0028 + 0.00225 = 0.00745.
So, the probability that a randomly bought vacuum cleaner produced by this company has a cord that does not meet the quality standard is approximately 0.00745, or about 0.745%.
To find the probability that the cord does not meet the quality standard, we need to consider the percentage of cords produced by each machine and the corresponding percentage of cords that do not meet the quality standard.
Let's calculate these probabilities step-by-step:
Step 1: Calculate the probability of selecting each machine:
The percentage of cords produced by each machine is given as follows:
- Machine 1: 20%
- Machine 2: 35%
- Machine 3: 100% - (20% + 35%) = 45%
Step 2: Calculate the probability of a cord produced by each machine not meeting the quality standard:
- Machine 1: 1.2%
- Machine 2: 0.8%
- Machine 3: 0.5%
Step 3: Calculate the overall probability that the cord does not meet the quality standard:
For each machine, multiply the probability of selecting that machine by the probability of a cord produced by that machine not meeting the quality standard. Then, sum up these probabilities:
Probability (cord from machine 1) = 20% * 1.2% = 0.20 * 0.012 = 0.0024
Probability (cord from machine 2) = 35% * 0.8% = 0.35 * 0.008 = 0.0028
Probability (cord from machine 3) = 45% * 0.5% = 0.45 * 0.005 = 0.00225
Total probability = Probability (cord from machine 1) + Probability (cord from machine 2) + Probability (cord from machine 3)
= 0.0024 + 0.0028 + 0.00225 = 0.00745
Therefore, the probability that a cord randomly selected from a vacuum cleaner produced by this company does not meet the quality standard is 0.00745, or 0.745%.
To find the probability that the cord does not meet the quality standard, we need to calculate the weighted average of the probabilities from each machine.
Step 1: Calculate the probability for each machine:
- Machine 1: 1.2% (0.012)
- Machine 2: 0.8% (0.008)
- Machine 3: 0.5% (0.005)
Step 2: Calculate the weighted average:
- Machine 1 contributes 20% (0.20) to the total production.
- Machine 2 contributes 35% (0.35) to the total production.
- Machine 3 contributes the remaining percentage, which is 100% - (20% + 35%) = 45% (0.45).
Now we multiply the probability for each machine by its corresponding percentage of production and sum them up:
(0.012 * 0.20) + (0.008 * 0.35) + (0.005 * 0.45) = 0.0024 + 0.0028 + 0.00225 = 0.00745
Therefore, the probability that the cord does not meet the quality standard is approximately 0.00745 or 0.745%.