How Do You Calculate the Range for Airline Bag Weights with 95% Confidence?

[cameuth]

Homework Statement

Suppose that the weights of airline passenger bags are normally distributed with a mean of 48.14 pounds and a standard deviation of 3.71 pounds.
Let X represent the weight of a randomly selected bag. For what value of c is P(E(X) - c < X < E(X) + c)=0.95? Give your answer to four decimal places.

Homework Equations

I have statcrunch and a normal, poisson, and gamma calculator.

The Attempt at a Solution

For this I assume we are looking for a standard deviation. I've been playing with a calculator but honestly I just need help getting started. thanks.

 

[Ninty64]

I think the best way to approach this problem is to visual what the problem is asking for. What is the region under the Normal Curve that it wants?

In this case, the symmetry could be of use to you.

 

[I like Serena]

You're looking at a confidence interval.

The formula for it is: $c = z^* \times \sigma$.
where z* is the critical z-value for the confidence level and $\sigma$ is the standard deviation.

For a confidence level of 0.95, z*=1.96, which you can find in any table for a standard normal distribution.