Answer to Question #301528 in Statistics and Probability for Mark

Question

 A 2-hour movie runs continuously at a local theater. You leave for the theater without first c checkingthe show times. Use an appropriate uniform density function to find the probability that you will arrive at the theater within 10 minutes of (before or after) the start of the film.

Answer 1

we have to define the probability of occurrence, before 10 minutes of starting of the movie or after 10 minutes of starting of the movie.

A movie runs continuously for 120 minutes. Let k be a random variable which measures the time of arrival. k is uniformly distributed over the time 0 ≤ t ≤ 120.

For this situation, the probability distribution function is

f(t) = (1/120) 0 ≤ t ≤ 120.

0, otherwise

The probability of occurrence, before 10 minutes of starting the movie is

$\int$₁₁₀¹²⁰ (1/120) dt

solving the above integral yields

(1/120 )= 0.0833 = 8.33%

Hence the probability of occurrence , before 10 minutes of the movie or after 10 minutes of starting of the movie is 0.0833= 8.33%