47. * A particularly long traffic light on your morning commute is green 20% of

Question

47. * A particularly long traffic light on your morning commute is green 20% of the time Or each of the following questions, begin by defining an appropriate random variable and state its distribution. IEM 3103 Class Notes. 12 Chapter 3. Discrete Random Variables Section 3.2. Mean and Variance of a Discrete Random Variable p. 13 (a) Over five mornings, what is the probability that the light is green on exactly one (b) Over 20 mornings, what is the probability that the light is green on exactly four (c) Over 20 mornings, what is the probability that the light is green on more than day? days? four days?

Explanation / Answer

Solution:-

p = 20/100

p = 0.20

This distribution is binomial, as there are two outcomes green light or non green. Each trial is indpendent.

a) Over five mornings , the probability that the light is green on exactly one day is 0.4096.

n = 5, x = 1

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 1) = 0.4096

b) Over 20 mornings , the probability that the light is green on exactly four day is 0.2182.

n = 20, x = 4

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 4) = 0.2182

c) Over 20 mornings , the probability that the light is green on more than four days is 0.6296.

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 4) = 0.6296

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