Answer:
- z for 184 = -2.2
- P(z < -2.2) ≈ 1.4%
- z for 200 = -0.6
- P(z < -0.6) ≈ 27.4%
- P(184 < x < 200) ≈ 26.0%
Step-by-step explanation:
Z is computed from ...
... z = (x -μ)/σ
Our lower limit for x is 184, so its z-value is ...
... z = (184 -206)/10 = -22/10 = -2.2
Our upper limit for x is 200, so its z-value is ...
... z = (200 -206)/10 = -6/10 = -0.6
A suitable table or probability calculator can tell you ...
... the percent of area associated with z = -2.2 is about 1.4%. That is, about 1.4% of all values lie below z = -2.2.
... the percent of area associated with z = -0.6 is about 27.4%.
The fraction of expenses between $184 and $200 is then calculated to be ...
... 27.4% - 1.4% = 26.0%
