Question

A manufacturing company uses two different machines, A and B, each of which produces a certain item part. The number of defective parts produced by each machine is about 1 percent. Suppose two independent random samples, each of size 100, are selected, where one is a sample of parts produced by machine A and the other is a sample of parts produced by machine B. Which of the following is true about the sampling distribution of the difference in the sample proportions of defective parts?
A The mean is 0 and the distribution is approximately normal
B The mean is 0 and the distribution will not be approximately normal
C The mean is 0.01 and the distribution is approximately normal
D The mean is 0.01 and the distribution will not be approximately normal.
Ε The mean is 1 and the distribution is approximately normal.

Answer 1

Answer:

B: The mean is 0 and the distribution will not be approximately normal

Step-by-step explanation:

It is true that the mean is 0 because it is the difference in the population proportions, 0.01−0.01. However, normality cannot be assumed because the sample sizes are not large enough.

Answer 2

The sample distribution is defined as the probability distribution of a given sample based on statistics.

The correct option is (a).

Given:

The defective parts produced by each machine is 1%.

The sample Size is 100.

Calculate the proportion of the defective parts.

$\dfrac{1}{100}=0.01$

Thus, the mean of each machine is 0.01.

Now, the mean difference between both machine is 0 and proportion will be normally distributed.

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