Q. 6.101 - Elementary Statistics

Question

Arterial Cord path. Umbilical cord blood analysis immediately after delivery is one way to measure the health of an infant after birth. Researchers G. Natalucci et al used it as a predictor of brain maturation of preterm infants in the article "Functional Brain

Maturation Assessed During Early Life Correlates with Anatomical Brain Maturation at Term-Equivalent Age in Preterm Infants " (Proly. are Resend, Vol. 74. No. 1. pp. 68-74). Based on this study. we will assume that, for preterm infants, the pH level of the arterial cord (one vessel in the umbilical cord) is normally distributed with a mean of 7.32 and a standard deviation of 0.1. Find the percentage of preterm infants who have arterial cord pH levels

a. between 7.0 and 7.5.

b. over 7.4.

Step-by-Step Solution

Answer

a) The percentage of preterm infants $=96.34 \%.$

b) The percentage of preterm infants $=21.19 \%.$

Step 1: Given Information (Part a)

Mean $\mu =7.32$

Standard deviation $\sigma =0.1$

Step 2: Explanation (Part a)

Find the $z$ score,

For $x=7$

      $z=\frac{x-\mu }{\sigma }$

 $$\begin{gathered} =\frac{7-7.32.}{0.1}\text{ for } \\ x=7.5 \end{gathered}$$

$=-3.2$

For $x=7.5$

$z=\frac{x-\mu }{\sigma }$

$=\frac{7.5-7.32}{0.1}$

$=1.8$

Area between z-scores

$=(\text{ area to the left of }1.8)-(\text{ Area to the left of-3.2) }$

$=0.9641-0.0007$

$=0.9634$

Step 1: Given Information (Part b)

Mean $\mu =7.32$

Standard deviation $\sigma =0.1$

Step 2: Explanation (Part b)

Find the z score,

For $x=7.4$

$z=\frac{x-\mu }{\sigma }$

$=\frac{7.4-7.32}{0.1}$

$=0.8$

Area to the right of z score

$=1-(\text{ area to the left of }0.8)$

$=1-0.7881$

$=0.2119$