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. Using the empirical rule, approximately what percent of red lights last between 2.5 and 3.5 minutes?

Percent of red lights last between 2.5 and 3.5 minutes is 95.44% .

Step-by-step explanation:

Step 1: Sketch the curve.

The probability that 2.5<X<3.5 is equal to the blue area under the curve.

Step 2:

Since μ=3 and σ=0.25 we have:

P ( 2.5 < X < 3.5 ) =P ( 2.5−3 <  X−μ < 3.5−3 )

⇒ P ( (2.5−3)/0.25 < (X−μ)/σ < (3.5−3)/0.25)

Since, Z = (x−μ)/σ , (2.5−3)/0.25 = −2 and (3.5−3)/0.25 = 2 we have:

P ( 2.5<X<3.5 )=P ( −2<Z<2 )

Step 3: Use the standard normal table to conclude that:

P ( −2<Z<2 )=0.9544

Percent of red lights last between 2.5 and 3.5 minutes is % .

10 - 75

step-by-step explanation:

there's nothing attached so it's most likely anything in that range.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: