Chapter 11.1, Problem 20E

(a)

To determine

To find: the percent of emergencies where the fire department arrives in $8$ minutes or less.

Answer to Problem 20E

In about $97.5\%$ emergencies fire department arrives at the scene in $8$ minutes or less.

Explanation of Solution

Given:

Mean is $6$ minutes

Standard deviation is $1$ minute.

Calculation:

The value $8$ represents $\mu +2\sigma$ , that is between two standard deviations above mean.

Now, comparing the first and second diagrams, the percentage of emergencies where fire department arrives at the scene in $8$ minutes or less is given by

  $0.15\%+2.35\%+13.5\%+34\%+34\%+13.5\%=97.5\%$

So, in about $97.5\%$ emergencies fire department arrives at the scene in $8$ minutes or less.

Conclusion:

Hence, $97.5\%$ emergencies fire department arrives at the scene in $8$ minutes or less.

(b)

To determine

To find: the percent of the time in which the fire department achieve its goal

Answer to Problem 20E

About $16\%$ of time the fire department achieves its goals.

Explanation of Solution

Given:

The goal to reach is $5$ minutes or less.

Calculation:

To find the percentage of emergencies where fire department arrives at the scene in $5$ minutes or less

The value $5$ represents $\mu +2\sigma$ , that is between one standard deviation below mean.

Now, comparing the first and second diagrams, the percentage of emergencies where fire department arrives at the scene in $5$ minutes or less is given by

  $0.15\%+2.35\%+13.5\%=16\%$

So, in about $16\%$ emergencies fire department arrives at the scene in $5$ minutes or less.

Thus, about $16\%$ of time the fire department achieves its goals.

Conclusion:

Thus, about $16\%$ of time the fire department achieves its goals.