Hello guys, I need your help please to solve 8 b. Thanks A company claims that 9

Question

Hello guys, I need your help please to solve 8 b. Thanks

A company claims that 98% of its manufactured components arc free of any defect. A consumer protection group decides to extensively investigate this claim and randomly selects and tests 1000 components, Assuming that the company's claim is true, how many components are expected to test defective? Find the (approximate) probability that at least 30 components test defective. EC: Suppose that this is indeed what happens; 30 or more components test defective. Do you agree with the company's claim? Explain.

Explanation / Answer

A)

Only 1 - 0.98 = 0.02 of the components are defective. Hence,

E(x) = n p = 1000*0.02 = 20 [ANSWER]

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b)

Here, the standard deviation of defective components is

standard deviation = sqrt(n p (1-p)) = sqrt(1000*0.02*(1-0.02)) = 4.427188724

By continuity correcttion or critical value here is 30-0.5 = 29.5.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    29.5      
u = mean =    20      
          
s = standard deviation =    4.427188724      
          
Thus,          
          
z = (x - u) / s =    2.14583127      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.14583127   ) =    0.015943221 [ANSWER]

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c)

No. This case is too rare for it to happen by chance. Then, it must be that the proportion of defectives must be more than 2%.

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