Question

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?

Answer 1

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