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

0.0753

Explanation

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

z-score is calculated with the next formula:

`z=(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=(400-580)/(125)=-1.44 \\ z_2=(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}`