Question

Based on a recent study, the pH level of the arterial cord (one vessel in the umbilical cord) is normally distributed with mean 7.26 and standard deviation of 0.13. 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 7.34. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. %. a. The percentage of arterial cord pH levels that are between 7.00 and 7.50 is (Round to two decimal places as needed.) %. b. The percentage of arterial cord pH levels that are over 7.34 is (Round to two decimal places as needed.)

Answer 1

Let X : pH level of arterial cord is normally distributed with

=7.26 and =0.13

a) we asked P( 7.00 < X < 7.50)

= P( (7.00-7.26)/0.13 < X-/ <( 7.50-7.26)/0.13)

= P( -2 < Z < 1.85)

= P( Z < 1.85) - P(Z<-2)

= 0.9687 - 0.0228

P( 7.00 < X < 7.50) = 0.945

Percentage = 94.50%

b)

P( X > 7.34) = P( X -/ > (7.34-7.26)/0.13)

= P( Z > 0.62)

= 1- P( Z < 0.62)

= 1 - 0.7324

P( X>7.34) = 0.2676

Percentage = 26.76%