Question

suppose taxi fare from logan airport to downtown boston is known to be normally distributed with a standard deviation of $2.50. the last seven times john has taken a taxi from logan to downtown boston, the fares have been $22.10, $23.25, $21.35, $24.50, $21.90, $20.75, and $22.65. what is a 95% confidence interval for the population mean taxi fare? multiple choice

Answer 1

The 95% confidence interval for the population mean taxi fare is approximately $19.97 to $24.95.

Step-by-step explanation:

We can use the formula for the confidence interval to find the 95% confidence interval for the population mean taxi fare:

CI = sample mean ± (Z * standard deviation / √sample size)

Given that the last seven taxi fares are $22.10, $23.25, $21.35, $24.50, $21.90, $20.75, and $22.65, the sample mean is $(22.10 + 23.25 + 21.35 + 24.50 + 21.90 + 20.75 + 22.65) / 7 = $22.46. The standard deviation is $2.50.

Now, we need to find the value of Z for a 95% confidence interval. For a 95% confidence interval, the Z value is approximately 1.96.

Substituting the values into the formula, we have:

CI = $22.46 ± (1.96 * $2.50 / √7)

Using a calculator, we can find the margin of error:

Margin of error = 1.96 * $2.50 / √7 ≈ $2.49

Therefore, the 95% confidence interval for the population mean taxi fare is approximately $19.97 to $24.95.