Chapter 2, Problem 9CRE

(a)

To determine

To find: the percent of as low birth weight babies.

Answer to Problem 9CRE

Approximately 1% of babies will be identified as having "low birth weight".

Explanation of Solution

Given:

Mean = 3668 grams

Standard deviation = 511 grams

Less than 2500 grams are known as low birth weight.

Calculation:

Babies that weigh less than 2500 grams at birth are classified as "low birth weight."

The objective is to find the percent of babies whose weight is less than 2500 grams.

The z-value that corresponds to a baby weight less than 2500 grams at birth is:

  $\begin{array}{l}z=\frac{2500-3668}{511}\\ =-2.29\end{array}$

The percent of babies weighing less than 2500 is equal to the area below that value -2.29. From standard normal table, the area below -2.29 is 0.0110.

  

Conclusion:

Hence, approximately 1% of babies will be identified as having "low birth weight".

(b)

To determine

To find: the quartiles of the birth weight distribution.

Answer to Problem 9CRE

The quartiles of the birth weight distribution are 3325.6 and 4010.4.

Explanation of Solution

Calculation:

It is supposed to find the quartiles of birth weight distribution. The z-value corresponding to the quartile $Q_1$ is $-0.67$ and the z-value corresponding to the quartile $Q_3$ is $0.67$ .

It is supposed to find the x -values corresponding to the quartiles.

The z -value corresponding to first quartile, $Q_1$ is given by

  $\begin{array}{l}-0.67=\frac{x-3668}{511}\\ \Rightarrow x=366-511\times 0.67\\ =3325.63\end{array}$

The z -value corresponding to third quartile $Q_3$ , is given by

  $\begin{array}{l}0.67=\frac{x-3668}{511}\hfill \\ \Rightarrow x=3668+0.67\times 511\hfill \\ =4010.37\hfill \end{array}$

Conclusion:

Hence, the quartiles of the birth weight distribution are 3325.6 and 4010.4.