Question

Add an intersection with a red light times are normally distributed with a mean Time of three minutes and a standard deviation of .25 minutes approximately what percent of my lights last between 2.5 and 3.5 minutes

Answer 1

2.5 and 3.5 are two standard deviations from the mean, since 2.5 = 3 - 2(0.25) and 3.5 = 3+2(0.25).

The empirical (68-95-99.7) rule says that approximately 95% of a normal distribution falls within two standard deviations of the mean.

Answer 2

Answer:

Required probability =0.95

Step-by-step explanation:

Let X be the intersection with red light times

X is Normal with mean = 3 and std dev = 0.25

We have to find out the probability of X lying between 2.5 and 3.5 minutes

P(2.5<x<3.5)

Let us convert these to Z score

$2.5$implies

$z>\frac{2.5-3}{0.25} \\z>-2$

Similarly $x\\z$

Hence required probability

=P($-2$