Question

A random sample of 380 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.

Answer 1

Number of component that will function properly = 380 - 30 = 350

Sample proportion of component that will function properly = 350 / 380 = 0.921

95% confidence interval for p is

- Z/2 * sqrt [ ( 1 - ) / n ] < p < + Z/2 * sqrt [ ( 1 - ) / n ]

0.921 - 1.96 * sqrt [ 0.921 * ( 1 - 0.921) / 380 ] < p < 0.921 + 1.96 * sqrt [ 0.921 * ( 1 - 0.921) / 380 ]

0.894 < p < 0.948

95% CI is ( 0.894 , 0.948 ) ​​​​​​​