A production manager randomly sampled production lines at a factory that produces automobiles. She wanted to find out how many production lines caused defects in newly produced automobiles. The proportion of production lines that caused defects was 0.08, with a margin of error of 0.01. Construct a confidence interval for the proportion of production lines that caused defects

The confidence interval for the proportion of production lines that caused defects is (0.07, 0.09).

Step-by-step explanation:

A confidence interval for a population proportion is a function of the sample proportion and the margin of error.

The interval has two bounds, a lower bound and an upper bound.

The lower bound is the sample proportion subtracted by the margin of error.

The upper bound is the margin of error added to the sample proportion.

In this problem, we have that:

Sample proportion 0.08

Margin of error 0.01

0.08 - 0.01 = 0.07

0.08 + 0.01 = 0.09

The confidence interval for the proportion of production lines that caused defects is (0.07, 0.09).

0.16 or 16%

step-by-step explanation:

lets take a coin for example.

if you toss it twice, it has a 1/4 chance of landing on heads both times because 1/2 * 1/2 is 1/4.

with the cards, the chance of picking dog is 0.4. having two people pick one is like picking a card twice in a row. so 0.4 * 0.4 is 0.16, or 16%