A survey of 50 retail stores revealed that the average price of a microwave was $375,with a sample standard deviation of $20. Assuming the population is normally distributed,what is the 95% confidence interval to estimate the true cost of the microwave?
A)$323.40 to $426.60
B)$328.40 to $421.60
C)$350.80 to $395.80
D)$369.31 to $380.69

Question

Quizplus · Accepted Answer

The 95% confidence interval for the mean can be calculated using the formula: $ \bar{x} \pm Z \frac{s}{\sqrt{n}} $, where $ \bar{x} $ is the sample mean, $ Z $ is the Z-score corresponding to the confidence level (for 95%, $ Z = 1.96 $), $ s $ is the sample standard deviation, and $ n $ is the sample size. Plugging in the given values: $ 375 \pm 1.96 \frac{20}{\sqrt{50}} $, we get the interval $ 369.31 $ to $ 380.69 $.

A Survey of 50 Retail Stores Revealed That the Average