Math215 Normal Distribution - Amount of Sleep | Complete Solution

Normal Distribution - Amount of Sleep
 
Do we humans get enough amount of sleep we need?
Here is what some experts are saying...
"There is increasing evidence that there is a very strong relationship between sleep quality and physical and mental health..."   A national survey of 31,044 adults revealed a link between insomnia and other sleeping problems with high blood pressure, heart failure, anxiety, and depression.  Experts say that there is no evidence yet to indicate that acquiring more sleep will improve medical conditions, but some studies have shown that more sleep makes teenagers do better in school.
The US National Sleep Foundation suggests that an adult needs seven to nine hours of sleep a night.  The Foundation conducted a survey in 2012 that suggested about 75% of Americans had sleeping problems, with one-third being so sleepy during the day that it affected their lives and activities.
On the other hand, when asked if everyone needed 8 hours of sleep each night, some experts stated:  "It's nonsense.  It's like saying everybody should have size eight shoes, or should wear Medium size clothes...  However, there is a normal distribution with the average sleep length seven and a quarter hours."  Many people report their sleeping hours more or less than the average, and that the determining factor for a required amount of sleep should be whether the person feels fresh and alert during the day, the same experts say.
While amount or quality of sleep undergoes a wide variety of changes during the human life span (based primarily upon age and life style), all aspects of sleep, at any given age, have a relatively normal, bell-shaped distribution.

After this motivational reading, now you will explore some sleep hours. First you need to collect a small data set in the following way.
a.    Record, to the nearest quarter of an hour, how many hours you slept in the past 24 hours. __________________
b.    Ask 3 more adults (in your family, in your classroom, at work, in the neighborhood, etc) how many hours of sleep they got in the past 24 hours and record their answers here to the nearest quarter of an hour.
___________________

___________________

___________________

c.    Use your data set and the results of the following survey to answer the questions that follow:

Questions:
Make sure you include your calculator command or your formula that you use to answer each question.
1.    What percent of adults from the survey slept longer than you did?

2.    How long did the person who slept the least in your data set (other than you) sleep? What percent of adults from the survey slept less than this person?

3.    How long did the person who slept the most in your data set (other than you) sleep? What percent of adults from the survey slept more than this person?

4.    A colleague at your work came late to the meeting this morning. He said that he overslept. When you asked, he reported that he slept about 8.5 hours. What percent of adults from the survey slept less than this person?
5.    Your boss, setting an example for the employees, said that he slept 6.75 hours last night to prepare for the meeting. What percent of adults from the survey slept longer than the boss?

6.    What percent of data in the survey lies in the interval from 5.5 hours to 8.5 hours?

7.    What interval about the mean includes 95% of the data in the survey?

8.    What interval about the mean includes 50% of the data in the survey?

9.    30% of adults in the survey sleep less than how many hours of sleep?

10.    10% of adults in the survey sleep more than how many hours of sleep?