Question

at an intersection, the red light light times are normally distributed with a mean time of 3 minutes and a standard deviation of 0.25 minutes. Approximately what percent of red lights last between 2.5 and 3.5 minutes

Answer 1

95.45%

Explanation:

To go about this, what we do is to calculate the z-scores of the values in the range given.

Mathematically;

z-scores = (x-mean)/SD

Here in this case , mean is 3 and standard deviation is 0.25

So for 2.5 minutes, we have ;

z-score = (2.5-3)/0.25 = -0.5/0.25 = -2

For 3.5 minutes, we have;

z-score = (3.5-3)/0.25 = 0.5/0.25 = 2

The required probability we want to calculate according to the range is thus;

P(-2<z<2)

We can calculate this value by the use of the standard normal table

Mathematically, we can have the above as;

P(-2<z<2) = P(z<2) - P(z<-2)

We proceed using the table and we have the values as follows;

P(-2<z<2) = 0.97725 - 0.02275 = 0.9545

Now the value 0.9545 in percentage would be 95.45%