A vehicle velocity check is conducted in a stretch of highway. On a regular weekday, the speeds were found to have a normal distribution with a mean of 52 and a standard deviation of 3. The daily average speeds for the same highway on consecutive normal weekdays were determined by sampling 25 vehicles each day. What is the two-standard deviation average speed?
To find the two-standard deviation average speed, we need to consider the concept of standard error. Standard error is the standard deviation of the sampling distribution. In this case, we are sampling 25 vehicles each day, so we need to calculate the standard error.
The formula for the standard error is:
Standard Error = Standard Deviation / √(Sample Size)
Given that the standard deviation is 3 and the sample size is 25, we can substitute these values into the formula to find the standard error:
Standard Error = 3 / √(25)
Standard Error = 3 / 5
Standard Error = 0.6
Now, to find the two-standard deviation average speed, we multiply the standard error by 2:
Two-Standard Deviation Average Speed = Standard Error * 2
Two-Standard Deviation Average Speed = 0.6 * 2
Two-Standard Deviation Average Speed = 1.2
Therefore, the two-standard deviation average speed is 1.2.