Answer:
0.1529
Step-by-step explanation:
Given that:
Probability of changing lane ; p = 45% = 0.45
Sample size (number of trials) = n = 7
Probability that atleast 5 vehicles will change lane :
Using the binomial probability formula :
P(x = x) = nCx * p^x * (1 - p)^(n-x)
(1 - p) = 1 - 0.45 = 0.55
P(x ≥ 5) = p(x = 5) + p(x = 6) + p(x = 7)
P(x = 5) = 7C5 * 0.45^5 * 0.55^2
P(x = 5) = 21 * 0.45^5 * 0.55^2 = 0.117221
P(x = 6) = 7C6 * 0.45^6 * 0.55^1
P(x = 6) = 7 * 0.45^6 * 0.55^1 = 0.031969
P(x = 7) = 7C7 * 0.45^7 * 0.55^0
P(x = 7) = 1 * 0.45^7 * 0.55^0 = 0.003736
P(x ≥ 5) = p(x = 5) + p(x = 6) + p(x = 7)
P(x ≥ 5) = 0.117221 + 0.031969 + 0.003736
P(x ≥ 5) = 0.152926
P(x ≥ 5) = 0.1529
