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Zorluk: OrtaExperimental and Theoretical Probability

A machine produces electronic components. Based on long-term specifications, the theoretical probability of producing a defective component is 0.040.04. In a quality control inspection, a random sample of 400400 components produced by the machine is tested, and 2222 are found to be defective. What is the absolute difference between the experimental probability and the theoretical probability of selecting a defective component from this sample?

Cevap: 0.015

Cevap

The absolute difference between the experimental probability and theoretical probability is 0.015.
The experimental probability is calculated from the trial outcomes as 22 divided by 400, which equals 0.055. Taking the absolute difference between this value and the theoretical probability of 0.04 gives |0.055 - 0.04| = 0.015.

Adım Adım Çözüm

1
Determine the experimental probability from the sample results
P(Experimental)=22400=0.055P(Experimental) = \frac{22}{400} = 0.055
Experimental probability is calculated as the ratio of observed successful outcomes (defective items found) to total trials (sample size).
2
Identify the given theoretical probability
P(Theoretical) = 0.04
Theoretical probability represents the expected likelihood under model specifications prior to sampling.
3
Subtract the theoretical probability from the experimental probability to find the absolute difference
|0.055 - 0.04| = 0.015
The absolute difference measures how much the observed empirical frequency deviates from the predicted model probability.

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Experimental vs Theoretical Probability
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Experimental and Theoretical Probability

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