Question

At an intersection, the red 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

Answer:

P = 95%

Step-by-step explanation:

The average is:

$\mu = 3\ minutes$

The standard deviation is:

$\sigma = 0.25\ minutes$.

We want the probability that the red light lasts between 2.5 minutes and 3.5 minutes

This is:

$P(2.5$

Now we must transform these values to those of a standard normal distribution to facilitate calculation by using the probability tables.

$P(2.5-3$

This is:

$P(-2$ ---------- (By the symmetry of the standard normal distribution)

When you search for the normal standard table, you get the following value:

$P(Z$