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

Answer:

95% of the confidence interval for q is

(0.05809 , 0.1183)

Step-by-step 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

                   $q^{-} = \frac{x}{n} = \frac{30}{340} = 0.0882$

Step:2

95% of the confidence interval is determined by

$(q - Z_{0.05} \sqrt{\frac{pq}{n} } , q + Z_{0.05} \sqrt{\frac{pq}{n} } )$

$((0.0804 -1.96 \sqrt{\frac{0.0804 X0.9118}{340} } ,0.0804 +1.96 \sqrt{\frac{0.0804 X0.9118}{340})$

$( 0.0882- 1.96 \sqrt{0.000236} , 0.0882 + 1.96 \sqrt{0.000236} )$

(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)