Normal Distribution of a chocolate bar

[Muffins]

Hey all, I was hoping you can help me out with a question I have trouble translating into math.

A factory manufactures chocolate bars with a declared weight of 100g per bar. In reality, the bars are normally distributed with expectation of 100g and SD of 5g.

It is demanded that no more than 4% deviates in more than 9.5g. Does our factory apply to these terms?

---

I started by defining random variable X to be the weight of a chosen chocolate bar.
X~N(100,5^2)

P(X<a)=0.04 ; φ(X<a)=0.04 -> φ(-X<a)=0.96 -> (X<a)=-1.751 -> a-100/5=-1.751 ; a=91.245 so that's the minimum weight allowance I think.

Is it just straight forward now, given that 100-9.5= 90.5 as the weight barrier for 4% of the batch? So, the factory applies to the standards?

Thanks in advance

 

[DrPhil]

Hey all, I was hoping you can help me out with a question I have trouble translating into math.

A factory manufactures chocolate bars with a declared weight of 100g per bar. In reality, the bars are normally distributed with expectation of 100g and SD of 5g.

It is demanded that no more than 4% deviates in more than 9.5g. Does our factory apply to these terms?

---

I started by defining random variable X to be the weight of a chosen chocolate bar.
X~N(100,5^2)

P(X<a)=0.04 ; φ(X<a)=0.04 -> φ(-X<a)=0.96 -> (X<a)=-1.751 -> a-100/5=-1.751 ; a=91.245 so that's the minimum weight allowance I think.

Is it just straight forward now, given that 100-9.5= 90.5 as the weight barrier for 4% of the batch? So, the factory applies to the standards?

Thanks in advance

When talking about "truth in packaging," it makes sense to use a single-tailed test - nobody is going to complain about getting too much chocolate. BUT the way the question is asked it looks like a two-tailed test - "deviates by more than 9.5 g" includes both plus and minus.

Your work for a single-tail test is correct. For two-tailed, repeat with P(X<a) = 0.02.