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Hello I was wondering If i can get some help with a question I am stuck...

Hello I was wondering If i can get some help with a question I am stuck on or more so a concept.

Formula: z = (x-μ)/(σ )
Σ = 1.1 lbs.
Μ = 4.1 lbs.
Z = (7 – 4.1) / 1.1 = 2.6 =.9953


This is what I get when I input my number in a normal distribution solver online= 0.0047

My issue is when calculating the Z number it seems like it will sometimes be negative and sometimes be positive to get the right answer. Could you explain how I can know when a z number will be negative or positive?

Below is the question I'm working and above is the work I have done for it.

Background Information: Atlantic mackerel are fish that grow to an average weight of 4.1 lb, with a standard deviation of 1.1 lb. We can assume that the weights of Atlantic mackerel are normally distributed.

a.)   (5 points) Your uncle claims that he once caught a 7 lb mackerel on a fishing trip. What is the probability of finding a mackerel that is 7 lb or larger? Round your answer to 4 digits after the decimal.

So I produced a positive 2.6 but it looks like to get the correct answer the 2.6 is negative according to the number we get from the z chart. If you could provide some clarification on this that would be much appreciated! Thank you!

math   Statistics-And-Probability   
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