Question

Suppose that the distribution of weekly water usage for single-family homes in a particular city is mound shaped and approximately symmetric. The mean is 1,500 gallons, and the standard deviation is 200 gallons. (Use the Empirical Rule.)
(a) What Is the approxlmate value In gal) of the 16th percentlle?
(b) What is the approximate value (In gal) of the medlan?
(c) What is the approximate value (In gal) of the 84th percentile?

Answer 1

Answer:

a. 1,300 gallons

b. 1,500 gallons

c. 1,700 gallons

Step-by-step explanation:

Data provided in the question

Mean = 1500 gallons

And, the Standard deviation = 200 gallons

Based on the above information as we know that

68 percent, 95 percent and 99.7 percent of data values are within 1 , 2 and 3 standard mean deviations, as per the empirical law.

The middle of 68% is the standard deviation mean that 68% lies within 1

68% lies within 1 standard deviation mean the middle 68% is between

= 1500 - 200

= 1,300 gallons

And

= 1500 + 200

= 1,700 gallons

Now

$= \frac{100 - 68}{2}$

= 16

Hence, bottom 16% is lower 1300 gallons

Now

Top 16% is upward 1700 gallons, i.e

= 100 - 16

= 84%

This bottom values are underneath 1700

So based on the above explanation

a) 16th percentile = 1,300 gallons

b) Median is

Since it is a Mean of symmetric mound shaped.  

Therefore,  Median is 1,500 gallons

c) 84th percentile is 1,700 gallons