As part of a quality control process for tortilla chips, an engineer at a factory randomly sampled 390 tortilla chips during a week of production to test the current rate of chips with severe defects (e.g. breaks instead of scooping up salsa). She finds that 78 of the chips are defective.

Calculate a 95% confidence interval for the proportion of all the chips produced that week that are defective. Please show the following steps.

Calculate the sample proportion.

Check both conditions for the Central Limit Theorem to hold.

Calculate the standard error.

Calculate the confidence interval.