There are four balls with the same size in a box. The balls are numbered 1, 2, 3 and 4. Sonya randomly picks up one ball, puts i
t back, and then randomly picks up one ball from the box. Let denote the sum of the numbers on the two balls she picked up. Find (round off to second decimal place).
1 answer:
Answer:
Explanation:
Here we have sampling with replacement. There are 4 x 4 = 16 out comes each with equal probability 1/16 .
The sample space being {1,2,3,4} {1,2,3,4} .
The random variable X representing the sum of the numbers on the balls has values from 2 to 8.
The other detailed steps and appropriate analysis is shown in the attached file.
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Answer:
Explanation:
The rate of production is determined by the slowest step or process.
Determine the rate of production of each step.
<em>1. The Cutting department has 6 machines that each process materials at a rate of 2 minutes per unit. </em>
- rate = number of machines × rate of each machince
- rate = 6 × 1 unit / 2 minute = 3 units / minute
<em>2. Drilling has 6 machines that each process materials at a rate of 3 minutes per unit. </em>
- rate = number of machines × rate of each machince
- rate = 6 × 1 unit / 3 minute = 2 units / minute
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<em>3. Stamping has 6 machines that each process materials at a rate of 4 minutes per unit. </em>
- rate = number of machines × rate of each machince
- rate = 6 × 1 unit / 4 minute = 1.5 units / minute
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<em>4. Welding has 4 machines that each process materials at a rate of 2 minutes per unit. </em>
- rate = number of machines × rate of each machince
- rate = 4 × 1 unit / 2 minute = 2 units / minute
<em>5. Painting has 2 machines that each process materials at a rate of 4 minutes per unit. </em>
- rate = number of machines × rate of each machince
- rate = 2 × 1 unit / 4 minute = 0.5 units / minute
Then, the fifth process, painting is the slowest process because it only can process 0.5 units per minute. This is the bottleneck. Even if the other processes worked faster, the production could not exceed the number of machines that can be painted per hour.
To find how many units can be painted or produced by hour multiply the rate by the number of minutes in one hour:
- 0.5 units/min × 60 min/hour = 30 units / hour.
Therefore, the capacity of the entire five-step process is 30 units per hour.