# 6.7 Normal distribution: homework  (Page 2/2)

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In the 1992 presidential election, Alaska’s 40 election districts averaged 1956.8 votes per district for President Clinton. The standard deviation was 572.3. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let $X=$ number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts )

• State the approximate distribution of $X$ . $X$ ~
• Is 1956.8 a population mean or a sample mean? How do you know?
• Find the probability that a randomly selected district had fewer than 1600 votes for President Clinton. Sketch the graph and write the probability statement.
• Find the probability that a randomly selected district had between 1800 and 2000 votes for President Clinton.
• Find the third quartile for votes for President Clinton.

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of 7 days.

• In words, define the random variable $X$ . $X=$
• $X$ ~
• If one of the trials is randomly chosen, find the probability that it lasted at least 24 days. Sketch the graph and write the probability statement.
• 60% of all of these types of trials are completed within how many days?
• The duration of a criminal trial
• $N\left(\text{21},7\right)$
• 0.3341
• 22.77

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.28 seconds . The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. (Source: log book of Terri Vogel)

• In words, define the random variable $X$ . $X=$
• $X$ ~
• Find the percent of her laps that are completed in less than 130 seconds.
• The fastest 3% of her laps are under _______ .
• The middle 80% of her laps are from _______ seconds to _______ seconds.

Thuy Dau, Ngoc Bui, Sam Su, and Lan Voung conducted a survey as to how long customers at Lucky claimed to wait in the checkout line until their turn. Let $X=$ time in line. Below are the ordered real data (in minutes):

 0.5 4.25 5 6 7.25 1.75 4.25 5.25 6 7.25 2 4.25 5.25 6.25 7.25 2.25 4.25 5.5 6.25 7.75 2.25 4.5 5.5 6.5 8 2.5 4.75 5.5 6.5 8.25 2.75 4.75 5.75 6.5 9.5 3.25 4.75 5.75 6.75 9.5 3.75 5 6 6.75 9.75 3.75 5 6 6.75 10.75
• Calculate the sample mean and the sample standard deviation.
• Construct a histogram. Start the $x-\text{axis}$ at $-0\text{.}\text{375}$ and make bar widths of 2 minutes.
• Draw a smooth curve through the midpoints of the tops of the bars.
• In words, describe the shape of your histogram and smooth curve.
• Let the sample mean approximate $\mu$ and the sample standard deviation approximate $\sigma$ . The distribution of $X$ can then be approximated by $X$ ~
• Use the distribution in (e) to calculate the probability that a person will wait fewer than 6.1 minutes.
• Determine the cumulative relative frequency for waiting less than 6.1 minutes.
• Why aren’t the answers to (f) and (g) exactly the same?
• Why are the answers to (f) and (g) as close as they are?
• If only 10 customers were surveyed instead of 50, do you think the answers to (f) and (g) would have been closer together or farther apart? Explain your conclusion.
• The sample mean is 5.51 and the sample standard deviation is 2.15
• $N\left(5\text{.}\text{51},2\text{.}\text{15}\right)$
• 0.6081
• 0.64

Suppose that Ricardo and Anita attend different colleges. Ricardo’s GPA is the same as the average GPA at his school. Anita’s GPA is 0.70 standard deviations above her school average. In complete sentences, explain why each of the following statements may be false.

• Ricardo’s actual GPA is lower than Anita’s actual GPA.
• Ricardo is not passing since his z-score is zero.
• Anita is in the 70th percentile of students at her college.

Below is a sample of the maximum capacity (maximum number of spectators) of sports stadiums. The table does not include horse racing or motor racing stadiums. (Source: http://en.wikipedia.org/wiki/List_of_stadiums_by_capacity )

 40,000 40,000 45,050 45,500 46,249 48,134 49,133 50,071 50,096 50,466 50,832 51,100 51,500 51,900 52,000 52,132 52,200 52,530 52,692 53,864 54,000 55,000 55,000 55,000 55,000 55,000 55,000 55,082 57,000 58,008 59,680 60,000 60,000 60,492 60,580 62,380 62,872 64,035 65,000 65,050 65,647 66,000 66,161 67,428 68,349 68,976 69,372 70,107 70,585 71,594 72,000 72,922 73,379 74,500 75,025 76,212 78,000 80,000 80,000 82,300
• Calculate the sample mean and the sample standard deviation for the maximum capacity of sports stadiums (the data).
• Construct a histogram of the data.
• Draw a smooth curve through the midpoints of the tops of the bars of the histogram.
• In words, describe the shape of your histogram and smooth curve.
• Let the sample mean approximate $\mu$ and the sample standard deviation approximate $\sigma$ . The distribution of $X$ can then be approximated by $X$ ~
• Use the distribution in (e) to calculate the probability that the maximum capacity of sports stadiums is less than 67,000 spectators.
• Determine the cumulative relative frequency that the maximum capacity of sports stadiums is less than 67,000 spectators. Hint: Order the data and count the sports stadiums that have a maximum capacity less than 67,000. Divide by the total number of sports stadiums in the sample.
• Why aren’t the answers to (f) and (g) exactly the same?
• The sample mean is 60,136.4 and the sample standard deviation is 10,468.1.
• $N\left(60136\text{.}\text{4},10468\text{.}\text{1}\right)$
• 0.7440
• 0.7167

## Try these multiple choice questions

The questions below refer to the following: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.

What is the median recovery time?

• 2.7
• 5.3
• 7.4
• 2.1

B

What is the z-score for a patient who takes 10 days to recover?

• 1.5
• 0.2
• 2.2
• 7.3

C

What is the probability of spending more than 2 days in recovery?

• 0.0580
• 0.8447
• 0.0553
• 0.9420

D

The 90th percentile for recovery times is?

• 8.89
• 7.07
• 7.99
• 4.32

C

The questions below refer to the following: The length of time to find a parking space at 9 A.M. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes.

Based upon the above information and numerically justified, would you be surprised if it took less than 1 minute to find a parking space?

• Yes
• No
• Unable to determine

A

Find the probability that it takes at least 8 minutes to find a parking space.

• 0.0001
• 0.9270
• 0.1862
• 0.0668

D

Seventy percent of the time, it takes more than how many minutes to find a parking space?

• 1.24
• 2.41
• 3.95
• 6.05

C

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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