Chapter 13, Problem 29RE

a.

To determine

What is the probability that the fire department takes to at most 8 minutes to arrive at the scene of an emergency?

Answer to Problem 29RE

  $P(x\le 8)=\mathrm{0.975.}$

Explanation of Solution

Given information: The time a fire department takes to arrive at the scene of an

emergency is normally distributed with a mean of 6 minutes and 4 standard deviation of 1 minute.

Calculation:

In term of the mean & standard deviation ,

  $\begin{array}{l}P(x\le 8)=P(x\le 6+2(1))\\ P(x\le 8)=P(x\le 6+2\sigma )\end{array}$

From the normal curve,

  

  $\begin{array}{l}P(x\le 8)=100\%-(2.35\%+0.15\%).\\ P(x\le 8)=97.5\%=\mathrm{0.975.}\end{array}$

b.

To determine

What is the probability that the fire department takes between 4 to 7 minutes to arrive at the scene of an emergency?

Answer to Problem 29RE

  $P(4\le x\le 7)=\mathrm{0.815.}$

Explanation of Solution

Given information: The time a fire department takes to arrive at the scene of an

emergency is normally distributed with a mean of 6 minutes and 4 standard deviation of 1 minute.

Calculation:

In term of the mean & standard deviation ,

  $\begin{array}{l}P(4\le x\le 7)=P(6-2(1)x\le 6+1).\\ P(4\le x\le 7)=P(\overline{x}-2\sigma \le x\le \overline{x}+\sigma ).\end{array}$

From the normal curve,

  

  $\begin{array}{l}P(4\le x\le 7)=13.5\%+2(34\%)=81.5\%.\\ P(4\le x\le 7)=81.5\%=\mathrm{0.815.}\end{array}$