Question

Babies born after 40 weeks gestation have a mean length of 52.2 centimeters (about 20.6 inches). Babies born one month early have a mean length of 47.4 centimeters. Assume both standard deviations are 2.5 centimeters and the distributions are unimodal and symmetric. (Source: www.babycenter) a. Find the standardized score (z-score), relative to all U.S. births, for a baby with a birth length of 45 centimeters

Answer 1

Answer:

  The standardized score (z-score), relative to all U.S. births, for a baby with a birth length of 45 centimeters is 2.88cm .                    

Step-by-step explanation:

It is given that the mean length of the babies born after the 40 weeks gestation period $(\bar{x})$ is 52.2cm

Standard deviation = 2.5

Baby born on one month earlier having mean length $(\bar{x_2})$ = 47.4cm

Now , we will use the formula for z-score ,

$z =\frac{x -\bar{x_1}}{s_1}$

$\frac{45-52.2}{2.5}$

= -2.88

Therefore , A birth length of 45 centimeters is 2.88 below the mean standard deviation.