Question Normal Distribution We have a normal probability di

Question Normal Distribution We have a normal probability distribution for variable x with = 42.79 and = 9.5. Determine the following (you may need to take averages between cells in the ztable):

(a) PDF(x = 32) (Equation, manual calculations in Excel, check with NORM.DIST(*,*,*,0) in Excel)

(b) P(x 21) (zscore, ztable, check with NORM.DIST(*,*,*,1) in Excel, use 5 decimal digits)

(c) P(37 x 60) (zscore, ztable, check with NORM.DIST(*,*,*,1) in Excel)

(e) P(x 57) (zscore, ztable, check with NORM.DIST(*,*,*,1) in Excel)

(f) x* so that P(x x*) = 0.9

Solution

a) PDF(x = 32) = 0.02203

b) P(x 21) =0.01090

c) P(37 x 60) =0.63843

d) P(x = 57) =0.06735

e) P(x x*) = 0.9

implies P(X x* ) = 1-0.9 = 0.1

implies x* = 35.11526

Note : All calculation are done using MS Excel as requested by you