Question

For a normally distributed population with mean =168 and st,dev = 23 Find the following probabilities.

A) P( Value between 160 and 174 ) or B) P( Value between 175 and 196 )

Which of the following is true.

a) They're the same

b) A is larger than B

c) B is larger than A

d) it's impossible to tell

Answer 1

c) B is larger than A

Solution:

We are given

Mean = 168

SD = 23

Part A

P(160<X<174) = P(X<174) – P(X<160)

Z = (X – mean)/SD

For X = 174

Z = (174 - 168)/23

Z = 0.26087

P(Z<0.26087) = P(X<174) = 0.602903

(by using z-table)

For X = 160

Z = (160 - 168)/23

Z = -0.34783

P(Z<-0.34783) = P(X<160) = 0.363985

(by using z-table)

P(160<X<174) = 0.602903 - 0.363985 = 0.238918

Required probability = 0.238918

Part B

P(175<X<196) = P(X<196) – P(X<175)

For X = 196

Z = (196 - 168)/23 = 1.217391

P(Z<1.217391) = 0.888272

(by using z-table)

For X = 175

Z = (175 - 168)/23 = 0.304348

P(Z<0.304348) = 0.619569

(by using z-table)

P(175<X<196) = 0.888272 - 0.619569 = 0.268703

Required probability = 0.268703

So, from above two parts, B is larger than A.