Use technology to solve the following problem: At a cell phone assembly plant, 81% of the cell phone keypads pass inspection. A random sample of 99 keypads is analyzed. Find the probability That the proportion of the sample keypads that pass inspection is between 0.74 and 0.86.
A) 0.8597
B) 0.9621
C) 0.0379
D) 0.8976

Question

Quizplus · Accepted Answer

We can use the normal distribution to solve this problem. First, we need to find the mean and standard deviation of the sampling distribution of the proportion.

Mean = 0.81 (given)
Standard deviation = sqrt((0.81*0.19)/99) = 0.0401

Next, we standardize the interval of interest:

Z1 = (0.74 - 0.81) / 0.0401 = -1.74
Z2 = (0.86 - 0.81) / 0.0401 = 1.39

Using a standard normal distribution table or calculator, we can find the probability that Z is between -1.74 and 1.39 to be approximately 0.8597.

Therefore, the answer is A, 0.8597.

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