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Zorluk: KolayStatistical Sampling and Studies

A quality control manager at a manufacturing plant selected a random sample of 150150 lightbulbs from a batch of 3,0003,000 lightbulbs produced on a certain day. The manager found that 66 of the selected lightbulbs were defective. Based on this sample, what is the estimated number of defective lightbulbs in the entire batch of 3,0003,000?

Cevap: 120 lightbulbs

Cevap

120
The correct answer is 120120. Since the sample of lightbulbs was selected at random, the proportion of defective lightbulbs in the sample can be used to estimate the proportion of defective lightbulbs in the entire batch. The proportion of defective lightbulbs in the sample is 6150=0.04\frac{6}{150} = 0.04. Multiplying this proportion by the total number of lightbulbs in the batch gives the estimated number of defective lightbulbs: 0.04×3,000=1200.04 \times 3,000 = 120.

Adım Adım Çözüm

1
Calculate the proportion of defective lightbulbs in the sample.
The sample proportion is 6150=0.04\frac{6}{150} = 0.04.
This establishes the rate of defects in the sample to be generalized to the entire batch.
2
Estimate the total number of defective lightbulbs in the batch.
The estimate is 0.04×3,000=1200.04 \times 3,000 = 120.
Scaling the sample proportion to the population size yields the expected number of defective lightbulbs in the entire batch.

Anahtar Kavram

Generalizing results from a random sample to estimate a population parameter
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Konular

Statistical Sampling and Studies

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