The mean length of...

Question

The mean length of angelfish is 8.8cm with standard deviation of 1.9cm. Assuming length is normal random variable, find the probability that a selected angelfish would be between 5.171cm and 7.109cm.

 

If someone could help me out with this problem that would be great! This is the type of question I'm stuck on.

Answer 1

It probably can be solved in this way:

 

z₁=(x-μ)/σ = (5.171-8.8)/1.9 = -1.91 with corresponding p-value from z table = 0.0281

z2=(x-μ)/σ = (7.109-8.8)/1.9 = -0.89  with corresponding p-value from z table = 0.1867

 

We need the probability between them, so it is 0.1867-0.0281 = 0.1586

 

So 15.86% would be bewteen 5.171 and 7.109.