Question 1111658
mean is 160cm and standard deviation is 15cm
:
working with a normal distribution, we calculate z-scores
:
a z-score = (X - mean)/standard deviation, where X is the value of the sample variable
:
i) Probability (P) ( X > 148) = 1 - P ( X < 148 )
:
z-score = (148 - 160)/15 = -0.8
:
lookup the z-score in the table of z-values to get its associated probability
:
P ( X < 148 ) = 0.2119
:
**********************************
P ( X > 148) = 1 - 0.2119 = 0.7881
**********************************
:
ii) P ( 155 < X < 165 ) = P ( X < 165 ) - P ( X < 155 )
:
z-score(165) = (165 - 160)/15 = 0.33
:
P( X < 165 ) = 0.6293
:
z-score(155) = (155 - 160)/15 = -0.33
:
P( X < 155 ) = 0.3707
:
**********************************************
P ( 155 < X < 165 ) = 0.6293 - 0.3707 = 0.2586
**********************************************
: