I am stuck on the first portion. We were given an answer sheet, but I don’t unde

Question

I am stuck on the first portion. We were given an answer sheet, but I don’t understand what 4!/2!(4-2)! is or how to put that in a calculator. Stat 201 Practice Exam On my morning commute, the traffic light on Gervais Street is green 20% of the time that I approach it. I know four days we have class: a. What is the probability that the light is green on exactly two days? (5 points) 1. is an independent trial, and want to know over the b. What is the probability that the light is green on more than two days? (5 points) On how many days can I expect to have a green light over the four days? (5 points) c.

Explanation / Answer

Solution:-

1) a) The probability that light is green on exactly two days is 0.1536.

By applying binomial distribution:-

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

P(x = 2) = 0.1536

b) The probability that light is green on more than two days is 0.0272.

By applying binomial distribution:-

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

P(x > 2) = 0.0272

c) The number of days we can expect to have a green light over the four days is 0.80.

E(x) = n × p

E(x) = 4 × 0.20

E(x) = 0.80

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