Given a normal distribution with mu = 35 and alpha = 7, find (a) the normal curv

Question

Given a normal distribution with mu = 35 and alpha = 7, find (a) the normal curve area to the right of x = 19; (b) the normal curve area to the left of x = 26; (c) the normal curve area between x = 41 and x = 48; (d) the value of x that has 80% of the normal curve area to the left; and (e) the two values of x that contain the middle 75% of the normal curve area. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table.

Explanation / Answer

here for normal distribution zscore =(X-mean)/std deviation

a)P(X>19)=1-P(X<19)=1-P(Z<(19-35)/7)=1-P(Z<-2.2857)=1-0.0111=0.9889

b)P(X<26)=P(Z<-1.2857)=0.0993

c)P(41<X<48)=P(0.8571<Z<1.8571)=0.9684-0.8043=0.1640

d)for 80- percentile ; z=0.8416

hence corresponding value=mean +z*std deviation =38.366

e) for middle 75% values , fall b/w 12.5% and 87.5% for which z=+/-1.1503

hence corresponding values =mean +/- z*std deviation =30.3986 ; 39.6014

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