Question

Based on a recent​ study, the pH level of the arterial cord​ (one vessel in the umbilical​ cord) is normally distributed with mean 7.32 and standard deviation of 0.11 Find the percentage of preterm infants who have the following arterial cord pH levels. a. pH levels between 7.00 and 7.50 b. pH levels over 7.40?

Answer 1

Solution :

Given that,

mean = = 7.32

standard deviation = = 15

a ) P (7.00 < x < 7.50 )

P ( 7.00- 7.32 / 0.11) < ( x -  / ) < ( 7.50 - 7.32 / 0.11)

P ( - 0.32 / 0.11 < z < 0.18/ 0.11)

P (-2.91< z < 1.64 )

P ( z < 1.64 ) - P ( z < -2.91)

Using z table

= 0.9495 - 0.0018

= 0.9477

Probability = 0.9477 = 94.77%

b ) P (x >  7.40)

= 1 - P (x < 7.40 )

= 1 - P ( x -  / ) < ( 7.40 - 7.32 / 0.11)

= 1 - P ( z < 0.08 /0.11 )

= 1 - P ( z < 0.73 )

Using z table

= 1 - 0.7673

= 0.2327

Probability = 0.2327 = 23.27%