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Vladimir79 [104]
3 years ago
9

Suppose that only 25% of all drivers come to a complete stop at an intersection having flashing red lights in all directions whe

n no other cars are visible. What is the probability that, of 20 ran- domly chosen drivers coming to an intersection under these conditions, a. At most 6 will come to a complete stop
Mathematics
1 answer:
alukav5142 [94]3 years ago
4 0

Answer:

The probability that at most 6 will come to a complete stop is 0.7857.

Step-by-step explanation:

Let <em>X</em> = number of drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible.

The probability of the event <em>X</em> is, P (X) = <em>p</em> = 0.25.

The sample of drivers randomly selected is of size, <em>n</em> = 20.

The random variable <em>X</em> follows a binomial distribution with parameters <em>n</em> = 6 and <em>p</em> = 0.25.

The probability function of  Binomial distribution is:

P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,...

Compute the probability that at most 6 will come to a complete stop as follows:

P (X ≤ 6) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)

                     + P (X = 4) + P (X = 5) + P (X = 6)

   ={20\choose 0}(0.25)^{0}(1-0.25)^{20-0}+{20\choose 1}(0.25)^{1}(1-0.25)^{20-1}+{20\choose 2}(0.25)^{2}(1-0.25)^{20-2}\\...+{20\choose 0}(0.25)^{6}(1-0.25)^{20-6}\\=0.0032+0.0211+0.0669+0.1339+0.1897+0.2023+0.1686\\=0.7857

Thus, the probability that at most 6 will come to a complete stop is 0.7857.

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