Question

the time spent waiting at a traffic light can be considered a random variable with values from 0 seconds, its green when you approach and can go on through, to 30 seconds with the following distribution shape: what is the height of this distribution? express your answer in decimal form using three decimal places. answer to three decimal places:

Explanation:

Step1: Identify Distribution Type

The waiting time at a traffic light with values from 0 to 30 seconds and a uniform distribution shape (as suggested by the rectangle) means it's a uniform distribution \( U(0, 30) \).

Step2: Recall Uniform Distribution Height Formula

For a uniform distribution \( U(a, b) \), the height (probability density function, PDF) is \( f(x)=\frac{1}{b - a} \) for \( a\leq x\leq b \), and 0 otherwise. Here, \( a = 0 \), \( b = 30 \).

Step3: Calculate the Height

Substitute \( a = 0 \) and \( b = 30 \) into the formula: \( f(x)=\frac{1}{30 - 0}=\frac{1}{30}\approx0.033 \) (rounded to three decimal places).

Answer:

\( 0.033 \)