An environmental group at a local college is conducting independent tests to determine the distance a particular make of automobile will travel while consuming only 1 gallon of gas.They test a sample of five cars and obtain a mean of 28.2 miles.Assuming that the standard deviation is 2.7 miles,find the 95 percent confidence interval for the mean distance traveled by all such cars using 1 gallon of gas.
A) [26.16,30.24]
B) [20.70,35.70]
C) [24.85,31.55]
D) [26.70,29.70]
E) [25.83,30.57]

Question

Quizplus · Accepted Answer

To find the 95% confidence interval for the mean distance traveled by all cars using 1 gallon of gas, we use the formula: 
CI = x̄ ± (zα/2) * (σ/√n)
where 
x̄ = 28.2 (sample mean)
σ = 2.7 (standard deviation)
n = 5 (sample size)
α = 0.05 (since we want a 95% confidence interval, the significance level is 1 - 0.95 = 0.05)
zα/2 = 1.96 (from the standard normal distribution table)

Plugging in the values, we get: 
CI = 28.2 ± (1.96) * (2.7/√5) 
CI = [24.85,31.55]

Therefore, the best choice is C ( [24.85,31.55] ).

An Environmental Group at a Local College Is Conducting Independent