Speeds for a randomly selected sample of n = 36 vehicles will be recorded. Determine the values that fill in the blanks in the following sentence. For samples of n = 36 vehicles, there is

about a 95% chance that the mean vehicle speed will be between ___ and ___.

What is the mean and standard deviation for the sample?

Z = (score-mean)/SEm

SEm = SD/√n

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (±.425) related to the Z score.

To determine the values that fill in the blanks, we need to use the concept of a confidence interval. A confidence interval provides a range of values within which we can be confident that the true population parameter falls. In this case, we want to find the confidence interval for the mean vehicle speed.

Step 1: Find the critical value
To calculate the confidence interval, we need the critical value, which depends on the desired level of confidence. Since we want a 95% confidence interval, we can look up the critical value from a standard normal distribution table.

For a 95% confidence interval, the critical value is approximately 1.96.

Step 2: Calculate the standard error
Next, we need to calculate the standard error of the mean, which is a measure of the variability in the sample mean. The formula for the standard error is:

SE = (standard deviation of the sample) / sqrt(sample size)

Since we don't have the standard deviation of the sample, we can estimate it by using the standard deviation of a similar sample or a previous study. Assuming we have the sample standard deviation, we can compute the standard error.

Step 3: Calculate the margin of error
The margin of error is the product of the critical value and the standard error. It represents the maximum amount of uncertainty we allow for estimating the true population mean. The formula for the margin of error is:

Margin of Error = Critical Value * Standard Error

Step 4: Calculate the confidence interval
Finally, we can calculate the confidence interval by subtracting and adding the margin of error to the sample mean.

Confidence Interval = Sample Mean ± Margin of Error

In this case, the sample mean would be the unknown value and the margin of error is the product of the critical value and the standard error.

Assuming you have the necessary data, apply the formulae above to fill in the blanks in the sentence to find the lower and upper bounds of the confidence interval for the mean vehicle speed.