Question

the distribution of waiting time for an elevator in an office building is shown below. what is the probability youll have to spend between 30 and 70 seconds waiting for the elevator? probability =

Explanation:

Step1: Identify the distribution type

The graph is a uniform distribution (rectangle) with minimum \( a = 0 \) and maximum \( b = 100 \) seconds. The height of the rectangle (probability density function, \( f(x) \)) for a uniform distribution is \( \frac{1}{b - a}=\frac{1}{100 - 0}=0.01 \), which matches the given height of \( 0.01 \).

Step2: Calculate the probability for the interval

For a uniform distribution, the probability \( P(c \leq X \leq d) \) is given by \( f(x)\times(d - c) \), where \( c = 30 \) and \( d = 70 \). Substitute the values: \( P(30 \leq X \leq 70)=0.01\times(70 - 30) \).

Step3: Compute the result

Calculate \( 70 - 30 = 40 \), then \( 0.01\times40 = 0.4 \).

Answer:

\( 0.4 \)