Not sure how to figure this out - Probability, Normal distribution

The normal distribution is commonly used to model the variability expected when making measurements. In this context, a measured quantity x is assumed to have a normal distribution whose mean is assumed to be the "true" value of the object being measured. The precision of the measuring instrument determines the standard deviation of the distribution.

a. If the measurements of the length of an object have a normal probability distribution with a standard deviation of 1 mm, what is the probability that a single measurement will lie within 2 mm of the true length of the object?

I don't know what formula to use here. I don't know what "true" value means so I'm not sure of the mean.

Can someone point me in the right direction?

medako said:

a normal distribution whose mean is assumed to be the "true" value

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It's in the problem statement.

Presumably, this means you have a specific value for the mean. In the problem statement, you don';t have a specific value. How would you proceed if you had a specific value for the mean?

tkhunny said:

It's in the problem statement.

Presumably, this means you have a specific value for the mean. In the problem statement, you don';t have a specific value. How would you proceed if you had a specific value for the mean?

Click to expand...

My initial thought was to try and find the Z value (x-mean)/sd but without knowing the mean or the x, I'm stuck.

That's very good. However, the problem statement already did that for you.

The standard deviation is 1 mm.

2 mm is two standard deviations.

The problem statement is concerned with 2 standard deviations on both sides of the mean.

You should have an Empirical Rule for that.

Pigeonhole Theory

My answer is 8 for the question below. What do you get?

There are 30 people in a restaurant. Each one of them ordered one or more of these dishes : Beef, Chicken & Pork. What is the minimum number of people who ordered the same dish or set of dishes?

Is my answer correct? Kindly advise please.