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:P = 95%Step-by-step explanation:The average is: [tex]\mu = 3\ minutes[/tex]The standard deviation is: [tex]\sigma = 0.25\ minutes[/tex]. We want the probability that the red light lasts between 2.5 minutes and 3.5 minutes This is: [tex]P(2.5 <X <3.5)[/tex]Now we must transform these values to those of a standard normal distribution to facilitate calculation by using the probability tables. [tex]P(2.5-3 <X- \mu<3.5-3)\\\\P(\frac{2.5-3}{0.25} <\frac{X- \mu}{\sigma}<\frac{3.5-3}{0.25})\\\\P(-2<Z<2)[/tex]This is: [tex]P(-2 <Z <2) = P(Z <2) - P(Z <-2)[/tex] ---------- (By the symmetry of the standard normal distribution) When you search for the normal standard table, you get the following value: [tex]P(Z <2) = 0.9772\\\\P(Z <-2) = 0.0228\\\\P(-2 <Z <2) = 0.9772 - 0.0228\\\\P(-2 <Z <2) = 0.9544[/tex]