Question

A random sample of 340 electronic components manufactured by a certain process are tested, and 30 are found to be defective. A device will be manufactured in which two of the components will be connected in series. The components function independently, and the device will function only if both components function. Let q be the probability that a device functions. Find a 95% confidence interval for q. Round the answers to three decimal places. The 95% confidence interval for q is (

Answer 1

95% of the confidence interval for q is

(0.05809 , 0.1183)

Explanation:

Step:1

Given that the random sample of 340 electronic components manufactured by a certain process is tested, and 30 are found to be defective.

sample proportion

`q^(-) = (x)/(n) = (30)/(340) = 0.0882`

Step:2

95% of the confidence interval is determined by

`(q - Z_(0.05) \sqrt{(pq)/(n) } , q + Z_(0.05) \sqrt{(pq)/(n) } )`

`((0.0804 -1.96 \sqrt{(0.0804 X0.9118)/(340) } ,0.0804 +1.96 \sqrt{(0.0804 X0.9118)/(340))`

`( 0.0882- 1.96 √(0.000236) , 0.0882 + 1.96 √(0.000236) )`

(0.0882 - 0.03011 , 0.0882+0.03011)

( 0.05809 , 0.1183)

Final answer:-

95% of the confidence interval for q is

(0.05809 , 0.1183)