Suppose hemoglobin level of teachers is normally distributed with the mean of 16 g/dL and a standard deviation of 2.4 g/dL.
a) What is the probability that the hemoglobin level of a teacher is between 13 and 22 g/dL?
b) What is the probability that the hemoglobin level of a teacher is more than 11 g/dL?
Solution :
Given that ,
mean = = 16
standard deviation = = 2.4
P(13< x <22 ) = P[(13-16) /2.4 < (x - ) / < (22-16) /2.4 )]
= P( -1.25< Z < 2.5)
= P(Z < 2.5) - P(Z <-1.25 )
Using z table
= 0.9938 - 0.1056
probability= 0.8882
B.
P(x > 11) = 1 - P(x< 11)
= 1 - P[(x -) / < (11-16) /2.4 ]
= 1 - P(z < -2.08)
Using z table
= 1 - 0.0188
= 0.9812
probability= 0.9812
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