SOLUTION: A manufacturing process produces 6.2% defective items. What is the probability that in a sample of 48 items: a. 11% or more will be defective?(Round the z-value to 2 decima

Question 1137234: A manufacturing process produces 6.2% defective items. What is the probability that in a sample of 48 items:

a. 11% or more will be defective?(Round the z-value to 2 decimal places and the final answer to 4 decimal places.)
b. less than 2% will be defective? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Rather than using a normal approximation, I would use a binomial, since np is <5
11% of 48 is 5.28, so want probability 6 or more are defective or 1-probabilty 5 or fewer are defective
0: 0.938^48=0.0463
1:48*0.062*0.938^47=0.1469
2: 48C2*0.062^2*0.938^46=0.2283
3: 48C3*0.062^3*0.938^45=0.2313
4: 48C4*0.062^4*0.938^44=0.1720
5: 0.1001
sum is 0.8786
so answer of question is 0.1214.
Fewer than 2% is fewer than 1 since 2% is 0.96
That is 0.938^48 or 0.0463 from above.
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