SOLUTION: the heights of students in a school has a normal distribution with a mean of 160cm and a standard deviation of 15cm. Find the probability that a student chosen at random (i) has a

Question 1111658: the heights of students in a school has a normal distribution with a mean of 160cm and a standard deviation of 15cm. Find the probability that a student chosen at random
(i) has a height that is greater than 148cm
(ii) has a height between 155cm and 165cm
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
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
**********************************************
:
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