Use technology to solve the following problem: At a cell phone assembly plant, 75% of the cell phone keypads pass inspection. A random sample of 110 keypads is analyzed. Find the probability That more than 78% of the sample keypads pass inspection.
A) 0.7958
B) 0.2337
C) 0.7663
D) 0.2042

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial distribution formula. Let X be the number of keypads that pass inspection in the sample. Then X has a binomial distribution with n = 110 and p = 0.75. We want to find P(X > 0.78*110). This can be approximated using the normal distribution with mean np = 82.5 and variance np(1-p) = 20.625. First, we standardize the value of 0.78*110:

(0.78*110 - 82.5) / sqrt(20.625) ≈ -1.26

Using a standard normal distribution table or calculator, we find the probability of Z > -1.26 to be approximately 0.7958. Therefore, the answer is choice B.

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