Question

g Suppose a movie starts at 5:00 p.m. and Lindsay, a customer who is always late, arrives at the movie theater at a random time between 5:10 p.m. and 5:55 p.m. Lindsay's late arrival time, in minutes, represented by X , models a uniform distribution between 10 and 55 min. Determine the height of the uniform density curve. Provide your answer with precision to three decimal places.

Answer 1

Answer:

We get the height of the uniform density curve:

$f_X(x)=0.022$

Step-by-step explanation:

We know that a movie starts at 5:00 p.m. and Lindsay, a customer who is always late, arrives at the movie theater at a random time between 5:10 p.m. and 5:55 p.m.

Therefore, we get a uniform distribution between 10 and 55 min.

$f_X(x)=\frac{1}{b-a}\\\\f_X(x)=\frac{1}{55-10}\\\\f_X(x)=\frac{1}{45}\\\\f_X(x)=0.022$

We get the height of the uniform density curve:

$f_X(x)=0.022$