Chapter 11.1, Problem 23E

To determine

To calculate:

The probability value that an individual will be late for the meeting at the bank

Answer to Problem 23E

The probability value that an individual will be late for the meeting at the bank is $6.68\%$

Explanation of Solution

Given information:

  $\begin{array}{l}\mu =8\\ \sigma =2\end{array}$

Formula used:

  $Z-$ Score is given by the following expression:

  $Z=\frac{x-\mu }{\sigma }$

Where,

Standard deviation: $\sigma$

Mean: $\mu$

Calculation:

Here, the problem states that there is no more than $11\min$ for an individual to make bank work and any meeting.

So, the probability value that the person will be late for the meeting is calculated by using the $Z-$ score formula:

  $\begin{array}{l}Z=\frac{x-\mu }{\sigma }\\ Z=1.5\end{array}$

Use the standard normal table to get the probability value at $Z-$ score:

  $P\left(z=1.5\right)=0.9332$

The probability value that the person will be late for the meeting is calculated as:

  $\begin{array}{l}P=1-0.9332\\ P=0.0668\\ P=6.68\%\end{array}$