Question

Suppose that the balance of a person’s bank account in Superior, WI is normallydistributed with mean $580 and standard deviation $125. Find the probability a random person from Superior has less than $400 or more than $1000 in their bank account.

Answer 1

Answer

0.0753

Step-by-step explanation

First, we need to compute the z-scores of the situations.

z-score is calculated with the next formula:

$z=\frac{x-\mu}{\sigma}$

where

• x: observed value

,

• μ: mean

,

• σ: standard deviation

Substituting μ = $580, σ = $125, x = $400, in one case, and x = $1000, in the other case, we get:

$\begin{gathered} z_1=\frac{400-580}{125}=-1.44 \\ z_2=\frac{1000-580}{125}=3.36 \end{gathered}$

The probability a random person from Superior has less than $400 or more than $1000 in their bank account is calculated as follows:

$P(z\lt-1.44\text{ or }z\gt3.36)=P(z\lt-1.44)+P(z\gt3.36)$

From the above table:

$P(z\lt-1.44)=0.0749$

From the above table:

$P(z\gt3.36)=1-0.9996=0.0004$

Substituting these results into the formula:

$\begin{gathered} P(z\lt-1.44\text{ or }z\gt3.36)=0.0749+0.0004 \\ P(z\lt-1.44\text{ or }z\gt3.36)=0.0753 \end{gathered}$