A large school district in Connecticut wants to estimate the average SAT score of this year's graduating class using a 95% confidence interval. The district takes a simple random sample of 100 seniors. The sample mean is 510 and the population standard deviation for SAT scores is known to be 75. What is the 95% confidence interval for µ?
Accepted Solution
A:
Answer: [ 502.5, 517.5]Step-by-step explanation:Given:Mean of the sample, µ = 510Total sample size, n = 100Standard deviation = 75Confidence level = 95%Now,The interval for µ is given as:⇒ µ ± [tex]z\frac{\sigma}{\sqrt n}[/tex]for 95% confidence level z value = 1.96Thus,The interval for µ⇒ 510 ± [tex]1.96\times\frac{75}{\sqrt{100}}[/tex]or⇒ 510 ± 7.5or⇒ [ 510 - 7.5, 510 + 7.5 ]or⇒ [ 502.5, 517.5]