Question

Traffic engineers studied the traffic patterns of two busy intersections on opposite sides of town at peak rush hour. At the first intersection, the average number of cars waiting to turn left was 17 with a standard deviation of 4 cars. At the second intersection, there was an average of 25 cars waiting to turn left with a standard deviation of 7 cars. The report combined the mean number of cars waiting to turn left at both intersections. Assuming the data are independent, the standard deviation of the sum is:

Answer 1

The standard deviation of the sum is of 8.06.

Explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Sum of normal variables:

When we add two normal variables, the mean is the sum of their means, and the standard deviation is the square root of the sum of their variances. In this question:

First intersection -> Standard deviation of 4

Second intersection -> Standard deviation of 7

Sum:

`\sigma = √(4^2 + 7^2) = √(65) = 8.06`

The standard deviation of the sum is of 8.06.