The state highway department is studying traffic patterns on one of the busiest highways in the state.As part of the study,the department needs to estimate the average number of vehicles that pass an intersection each day.A random sample of 64 days gives us a sample mean of 14,205 cars and a sample standard deviation of 1,010 cars.After calculating the confidence interval,the highway department officials decide that the precision is too low for their needs.They feel the precision should be 300 cars.Given this precision,and needing to be 99% confident,how many days do they need to sample?
A)109
B)76
C)75
D)62
E)9

Question

Quizplus · Accepted Answer

To achieve a desired precision with a 99% confidence level, the sample size can be calculated using the formula for the confidence interval: n = (Z * σ / E)^2, where Z is the Z-score for 99% confidence (approximately 2.576), σ is the standard deviation (1,010), and E is the desired margin of error (300). Plugging in these values gives n ≈ 76.

The State Highway Department Is Studying Traffic Patterns on One