SOLUTION: I am trying to solve a two part statistics question. A mechanical press is used to mold shapes for plastic toys. when the machine is adjusted and working well, it still produce

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Question 935955: I am trying to solve a two part statistics question.
A mechanical press is used to mold shapes for plastic toys. when the machine is adjusted and working well, it still produces about 8% defective toys. The toys are manufactured in lots of n=100. Let r be a random variable representing the number of defective toys in the lot. Then p(hat) = r/n is the proportion of defective toys in a lot.
a. Find P(.07<=p(hat) <=.09). Round to the nearest 4 decimal places.
b. Find the probability that between 7 and 9 defective toys produced in the lot n=100 toys. That is, find P(7<=r<=9) remembering to use the continuity correction of +-0.5.
I am assuming that sigma is the square root of npq, n=100, q=1=p, how do I find p(hat) if I don't have r.
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
A mechanical press is used to mold shapes for plastic toys. when the machine is adjusted and working well, it still produces about 8% defective toys. The toys are manufactured in lots of n=100. Let r be a random variable representing the number of defective toys in the lot. Then p(hat) = r/n is the proportion of defective toys in a lot.
a. Find P(.07<=p(hat) <=.09). Round to the nearest 4 decimal places.
Solution:
.05/100 = .005
The z-score for .065 is %280.065-0.08%29%2Fsqrt%28%280.08%29%2A%281-0.08%29%2F100%29 =-0.5529
The z-score for .095 is %280.095-0.08%29%2Fsqrt%28%280.08%29%2A%281-0.08%29%2F100%29 = 0.5529
P(-0.5529 < Z < 0.5529) = highlight%280.4197%29 [Answer]
b. Find the probability that between 7 and 9 defective toys produced in the lot n=100 toys. That is, find P(7<=r<=9) remembering to use the continuity correction of +-0.5.
The z-score for 6.5 is %286.5-8%29%2Fsqrt%28100%2A%280.08%29%2A%281-0.08%29%29 = -0.5529
The z-score for 9.5 is %289.5-8%29%2Fsqrt%28100%2A%280.08%29%2A%281-0.08%29%29 = 0.5529
P(-0.5529 < Z < 0.5529) = highlight%280.4197%29 [Answer]