Chapter 6: Q. 6.41 (page 262)

Ages of Mothers. From the document National Vital Statistics Reports, a publication of the National Centre for Health Statistics, we obtained the following frequency distribution for the ages of women who became mothers during one year.
a. Obtain a relative-frequency histogram of these age data.
b. Based on your histogram, do you think that the ages of women who became mothers that year are approximately normally distributed? Explain your answer.

Short Answer

Expert verified

Part $(a)$ : A relative-frequency histogram of the given age data is,

Part $(b)$ : Yes, I think that the ages of women who became mothers that year are approximately normally distributed.

Step by step solution

Part a Step 1. Given information

Part a Step 2. The frequency and the relative frequency distributions for age is shown in the following table:

Age (yrs)	Frequency $f$	Relative Frequency
$10 - 15$	$7, 315$	$0.0018$
$15 - 20$	$425, 493$	$0.1045$
$20 - 25$	$1, 022, 106$	$0.2511$
$25 - 30$	$1, 060, 391$	$0.2605$
role="math" localid="1652525429747" $30 - 35$	$951, 219$	$0.2336$
$35 - 40$	$453, 927$	$0.1115$
role="math" localid="1652525460018" $40 - 45$	$95, 788$	$0.0235$
$45 - 50$	$54, 872$	$0.0135$
Total	$4, 071, 111$	$1.0000$

Part a Step 3. A relative frequency histogram of the given age data:

Part b Step 1. Explanation for the answer:

Yes, I think that the ages of women who became mothers that year are approximately normally distributed. It shows that the distribution of age has roughly the shape of normal curve and consequently, that the variable "age" is approximately normally distributed for this population.