a used car dealer wants to know the mean mileage of the cars currently in his lot. Rather than checking all of the cars, he samples 25 cars and finds that the mean mileage of the sample is 12,456.25. Assuming a standard deviation of 225 miles a confidence level of 95%, what is the margin of error for the sample mean? Use z=1.960

Question

a used car dealer wants to know the mean mileage of the cars currently in his lot. Rather than checking all of the cars, he samples 25 cars and finds that the mean mileage of the sample is 12,456.25. Assuming a standard deviation of 225 miles a confidence level of 95%, what is the margin of error for the sample mean? Use z=1.960

answers-
17.64
52.6
88.2
104.67

Thanks for the help in advance

Answer 1

To find the margin of error for the sample mean, you can use the formula:

Margin of Error = Z * (Standard Deviation / √(Sample Size))

where Z is the critical value corresponding to the desired confidence level, the Standard Deviation is the population standard deviation, and the Sample Size is the number of observations in the sample.

Given that the confidence level is 95% and the critical value is Z = 1.960, the standard deviation is 225 miles, and the sample size is 25, we can plug these values into the formula:

Margin of Error = 1.960 * (225 / √(25))

Simplifying the equation:

Margin of Error = 1.960 * (225 / 5)

Calculating the value:

Margin of Error = 1.960 * 45

Margin of Error ≈ 88.2

Therefore, the margin of error for the sample mean is approximately 88.2 miles. So, the correct answer is option C - 88.2.