Answer:
0.75 = 75% probability that he will have to wait at a red light for more than 15 seconds
Step-by-step explanation:
At each second, the stoplight is equally likely to change, which means that we use the uniform probability distribution to solve this question.
Uniform probability distribution:
Has two bounds, a and b. The probability of finding a value higher than x is given by:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Red for 60 seconds
So when Jamal arrives it can change in any number of seconds between 0 and 60, that is, [tex]a = 0, b = 60[/tex]
Probability that he will have to wait at a red light for more than 15 seconds?
[tex]P(X > 15) = \frac{60 - 15}{60 - 0} = \frac{45}{60} = \frac{3}{4} = 0.75[/tex]
0.75 = 75% probability that he will have to wait at a red light for more than 15 seconds
