Probability and standard deviation Question

[Potatochip911]

Homework Statement

A business owner makes jars with weights that follow a normal distribution with a standard deviation of 8 pounds. In a random sample of 64 jars what is the probability that the sample mean differs from the population mean by no more than 1 pound?

Homework Equations

$z=\frac{x-\bar{x}}{\frac{\sigma}{\sqrt{n}}}$

The Attempt at a Solution

n=64
$\sigma$=8
mean=$b$
$z_{2}=\frac{(b+1)-b}{\frac{8}{\sqrt{64}}}=0.125$
$z_{1}=\frac{(b-1)-b}{\frac{8}{\sqrt{64}}}=-0.125$
$P(-0.125<z<0.125)=P(z<0.125)-P(z<-0.125)=0.1232$
Not really sure what I'm doing wrong here but this is not even close to the correct answer.
Edit: Well this is really embarrassing I did the actual arithmetic wrong lol its 1/1 and -1/1 not 1/8 and -1/8

 

[Mark44]

Homework Statement

A business owner makes jars with weights that follow a normal distribution with a standard deviation of 8 pounds. In a random sample of 64 jars what is the probability that the sample mean differs from the population mean by no more than 1 pound?

Homework Equations

$z=\frac{x-\bar{x}}{\frac{\sigma}{\sqrt{n}}}$

The Attempt at a Solution

n=64
$\sigma$=8
mean=$b$
$z_{2}=\frac{(b+1)-b}{\frac{8}{\sqrt{64}}}=0.125$
$z_{1}=\frac{(b-1)-b}{\frac{8}{\sqrt{64}}}=-0.125$
$P(-0.125<z<0.125)=P(z<0.125)-P(z<-0.125)=0.1232$
Not really sure what I'm doing wrong here but this is not even close to the correct answer.
Edit: Well this is really embarrassing I did the actual arithmetic wrong lol its 1/1 and -1/1 not 1/8 and -1/8

So you have been able to figure this out?

 

[Potatochip911]

So you have been able to figure this out?

Yea I just messed up the arithmetic so that was giving me the wrong Z values.