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Step-by-step explanation:

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2 years ago

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At an intersection, the red-light times are normally distributed with a mean time of 3 minutes and a standard deviation of 0.25

denpristay [2]

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

<u>Step-by-step explanation:</u>

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 $0.9544(100) = 95.44$ % .

3 0

2 years ago

1. There are 125 juniors at the high school.How many ways can they elect a

valentinak56 [21]

Answer: 1. 1,906,500

2. 840

Step-by-step explanation:

1. Given: There are 125 juniors at the high school.

Total positions = 3 [president,vice president, and secretary]

Then, Number of ways to elect a president,vice president, and secretary( which is in order) out of 125 juniors = $^{125}P_{3}=\dfrac{125!}{(125-3)!}$ [Using permutations]