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ohaa [14]
4 years ago
13

A manufacturer of cellular phones has decided that an assembly line is operating satisfactorily if less than​ 6% of the phones m

anufactured per day are defective. To check the quality of a​ day's production, the company decides to randomly sample 30 phones from a​ day's production and test for defects. Define the population of interest to the manufacturer.
a. All the phones produced during the day in question.
b. The 30 phones sampled and tested.
c. The 30 responses: defective or not defective.
d. The 3% of the phones that are defective.
Mathematics
1 answer:
ludmilkaskok [199]4 years ago
6 0

Answer:

a) All the phones produced during the day in question.

Step-by-step explanation:

In statistics, the Population is all the objects with the same characteristics in which we have an interest in doing an experiment or statistical analysis. Sometimes to make it more simple, we take just a sample of the population and we do the experiments with them, and then the answers are used to all of the objects.

In this case, they want to analyze all the cellphones but they only take a few to do it. So the answer is a) All the phones produced during the day in question.

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Step-by-step explanation:

Let <em>X</em> = number of items with unacceptable quality.

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The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 150 and <em>p</em> = 0.05.

According to the Central limit theorem, if a sample of large size (<em>n</em> > 30) is selected from an unknown population then the sampling distribution of sample mean can be approximated by the Normal distribution.

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The standard deviation of this sampling distribution is: \sigma_{\hat p}=\sqrt{\frac{ p(1-p)}{n}}=\sqrt{\frac{0.05(1-.0.05)}{150} }=0.0178

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*Use a <em>z</em>-table for the probability.

Thus, the probability that at most 10 of the next 150 items produced are unacceptable is 0.8315.

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