Question

The fire department records how long it takes each of its trucks to reach the scene of a fire. Suppose that distribution of arrival times is uniform with the minimum time being 2 minutes and the maximum 15 minutes. Let Y equal the time it takes a truck to arrive at the scene of a fire after being called.

What is the probability that a truck will reach a fire scene within 5 to 10 minutes?

What is the expected time until arrival of the fire truck?

What is the standard deviation of truck arrival times?

Answer 1

Solution :

Given that ,

a = 2

b = 15

a)

Probability

P( c < X < d ) = ( d - c ) / ( b - a )

P( 5 < X < 10 ) = ( 10 - 5 ) / ( 15 - 2 )

P( 5 < X < 10 ) = 0.3846

The probability that a truck will reach a fire scene within 5 to 10 minutes is 0.3846

b)

Mean = ( a + b ) / 2

= ( 2 + 15 ) / 2

= 8.5

The expected time until arrival of the fire truck is 8.5

c)

Standard deviation = ( b - a )² / 12

= ( 15 - 2 ) ² / 12

= 3.7528

The standard deviation of truck arrival times is 3.7528