The following frequency distribution presents the five most frequent reasons for hospital admissions in U. S. community hospitals in a recent year. Reason Frequency (in thousands)
Congestive heart failure    990
Coronary atherosclerosis 1400
Heart attack   744
Infant birth 3800

Required:
a. Construct a frequency bar graph.
b. Construct a relative frequency distribution.
c. Construct a relative frequency bar graph.
d. Construct a relative frequency Pareto chart.

See Explanation

Step-by-step explanation:

Given

Solving (a): Frequency bar graph

To do this, we simply plot the reasons (on the x-axis) against the frequency (on the y-axis).

See attachment

Solving (b): Relative frequency distribution

The relative frequency is calculated as:

Where

So, we have:

So, the relative distribution is:

Solving (c): Relative frequency bar graph

To do this, we simply plot the reasons (on the x-axis) against the relative frequency (on the y-axis).

See attachment

Solving (d): Relative frequency Pareto chart

First, calculate the cumulative relative frequency

This is done by adding up the previous relative frequency,

So, we have:

So, we have:

Next, we simply plot the reasons (on the x-axis) against the cumulative relative frequency (on the right) and the left of the Pareto chart.

See attachment

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)