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:
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
[tex]2.5<x[/tex]implies
[tex]z>\frac{2.5-3}{0.25} \\z>-2[/tex]
Similarly [tex]x<3.5 -->\\z<\frac{3.5-3}{0.25} \\=2[/tex]
Hence required probability
=P([tex]-2<z<2) =2(0.475)\\=0.95[/tex]
