Answer:
a) Z-score = 0.75
b) Z-score = -32.833
Step-by-step explanation:
Step(i):-
Given that mean of the Population = 33
Given a standard deviation of the Population = 12
Let 'X' be a random variable in a normal distribution
Let 'X' = 42
Step(ii):-
[tex]Z = \frac{x-mean}{S.D}[/tex]
[tex]Z = \frac{42-33}{12} = 0.75[/tex]
Step(iii):-
Given that mean of the Population = 89
Given a standard deviation of the Population = 1
Let 'X' be a random variable in a normal distribution
Let 'X⁻ = 82
[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{82-89}{\frac{1}{\sqrt{22} } } = -32.833[/tex]
Z-score = -32.833
