Question

A civil engineer is studying a left-turn lane that is long enough to hold seven cars. Let X be the number of cars in the line at the end of a randomly chosen red light. The engineer believes that the probability that X = x is proportional to (x + 1)(8 − x) for x = 0, . . . , 7 (the possible values of X), i.e. P(X = x) = ( C(x + 1)(8 − x) for x = 0, 1, . . . , 7 0 otherwise 1. Determine the value of C. 2. Find the probability that X will be at least 5.

Answer 1

Answer:

a) C= 1/120

b) P(X>=5) = 0.333

Explanation:

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Answer 2

Answer:

A) C = 1/120

B) P( x ≥ 5) = 1/3

Explanation:

I've attached explanations to this.