a. "P(Z<z)=0.05\\to z=-1.645\\to -1.645=\\frac{x-32}{1.5}\\to x=29.5."
"P(Z>z)=0.05\\to z=1.645\\to 1.645=\\frac{x-32}{1.5}\\to x=34.5"
The heights less than 29.5 in and greater than 34.5 in could be a problem.
b.
(i) "P(X>36)=P(Z>\\frac{36-32}{1.5})=P(Z>2.67)=0.0038."
(ii) "P(X<34)=P(Z<\\frac{34-32}{1.5})=P(Z<1.33)=0.9082."
(iii)
"P(30<X<33)=P(\\frac{30-32}{1.5}<Z<\\frac{33-32}{1.5})=\\\\=P(-1.33<Z<0.67)=0.6568."
Comments
A very clear and good work which is easy to understand.
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