Question

It is known that the height (X) of females in a certain country is normally distributed with mean μ = 1600 millimeters (mms) and standard deviation σ = 63 mms. Use the normal distribution to calculate the proportion of females who are at least 1553 and at most 1621 millimeters tall, i.e. P( 1553 < X < 1621 ) Answer to four decimal place.

Answer 1

P ( 1553 < X < 1621 )
Standardizing the value

Z = ( 1553 - 1600 ) / 63
Z = -0.75
Z = ( 1621 - 1600 ) / 63
Z = 0.33
P ( -0.75 < Z < 0.33 )
P ( 1553 < X < 1621 ) = P ( Z < 0.33 ) - P ( Z < -0.75 )
P ( 1553 < X < 1621 ) = 0.6306 - 0.2278
P ( 1553 < X < 1621 ) = 0.4027