Q.6.41 - Elementary Statistics

Question

The National Center for Health Statistics publishes information about birth rates (per 1000 population) in the document National Vital Statistics Report. The following table provides a frequency distribution for birth rates during one year for the 50 states and the District of Columbia.

a. Obtain a frequency histogram of these birth-rate data.

b. Based on your histogram, do you think that birth rates for the $50$ states and the District of Columbia are approximately normally distributed? Explain your answer.

Step-by-Step Solution

Answer

(a)

(b)  The variable 'age' is nearly normally distributed in this group. 

Part (a) Step 1: Given information

Given in the question that, The National Center for Health Statistics publishes information about birth rates (per 1000 population) in the document National Vital Statistics Report. The following table provides a frequency distribution for birth rates during one year for the 50 states and the District of Columbia.

We need to obtain a frequency histogram of these birth-rate data. 

Part (a) Step 2: Explanation

The following table shows the frequency and relative frequency distributions for age:

Age (yrs)	Frequency $f$	Relative frequency
$10-15$	$7,315$	0.0018
$10-15$	425,493	0.1045
15-20	1,022,106	0.2511
20-2525-30	1,060,391	0.2605
30-35	951219	0.2336
35-40	453,927	0.1115
40-45	95,788	0.0235
45-50	54,872	0.0135
Total	4,071,111	1.0000

The age of a woman who became a mother within a year has the following relative frequency histogram:

The age of a woman who became a mother within a year has the following relative frequency histogram:

Part (b) Step 1: Given information

Given in the question that, The National Center for Health Statistics publishes information about birth rates (per 1000 population) in the document National Vital Statistics Report. The following table provides a frequency distribution for birth rates during one year for the 50 states and the District of Columbia.

 

Based on the histogram we need to find that whether the birth rates for the $50$ states and the District of Columbia are approximately normally distributed.

Part (b) Step 2: Explanation

The following table shows the frequency and relative frequency distributions for age:

Age (yrs)	frequency   $f$	Relative frequency
width="52" style="max-width: none; vertical-align: -4px;" $10-15$	width="42" style="max-width: none; vertical-align: -4px;" $7,315$	width="51" style="max-width: none; vertical-align: -4px;" $0.0018$
width="52" style="max-width: none; vertical-align: -4px;" $15-20$	width="60" style="max-width: none; vertical-align: -4px;" $425,493$	width="51" style="max-width: none; vertical-align: -4px;" $0.1045$
width="52" style="max-width: none; vertical-align: -4px;" $20-25$	$1,022,106$	$0.2511$
$25-30$	$1,060,391$	$0.2605$
$30-35$	$951,219$	$0.2336$
$35-40$	$453,927$	$0.1115$
$40-45$	$95,788$	$0.0235$
$45-50$	$54,872$	$0.0135$
Total	$4,071,111$	$1.0000$

The age of a woman who became a mother within a year has the following relative frequency histogram:

The following table shows an age distribution that resembles a normal curve, showing that the variable 'age' is almost normally distributed in this group.