Mary,
I think that drawing a diagram helps clarify what is being asked. This is a normal distribution so the curve is "bellshaped" but you don't know the mean so you can't place the Yaxis. The area under the curve is 1 and the area under the curve to the left of 78 is quite small, 5.48%, that is 0.0548, so 78 must be quite far to the left. I am going to use X for the random variable.
To use the area under the curve value, 0.0548, you are going to need to use the standard normal table so you need to convert X to the standard normal variable Z. You know the standard deviation is 5 so the transformation is
Z = ^{(X  )}/_{} = ^{(X  )}/_{5}
and the diagram becomes
Now I need to find 0.0548 in the standard normal table. My table reads areas to the right of the value so when I look for 0.0548 I find a Zvalue of 1.6
Since the normal distribution is symmetric about the mean
1.6 = ^{(78  )}/_{5}
Solve for .
Penny
