Download Extra Credit Assignment

Assignment 6 (38 Point)
Chapters 11 – 13
Fall 2014
Math 018
Name___________________________________
Directions: Read each question carefully and answer as clearly as possible. Place your answers on the given space(s) and
staple all work to the back of the page. All work must be included in order to receive credit. Please have work organized
neatly.
st
Due Date: Start of class on Friday, November 21 , 2014
Encouraging Quote: “Someone done stoled my wheels.”---Cletus
1.
For mallard ducks and Canadian geese, what percentage of nests are successful nests? A successful nest is described
as a nest where at least one offspring survives. Studies in Montana, Illinois, Wyoming, Utah and California gave the
following percentages of successful nests.
Mallard Ducks
Location
Percentage
Montana
56
Illinois
85
Wyoming
52
Utah
13
California
39
Montana
24
Illinois
49
Wyoming
60
Utah
69
California
18
Canadian Geese
Location
Percentage
a.
(4 Points) Find the sample mean and sample standard deviation for the percentage of Mallard Ducks nests
which are successful. Round the standard deviation to one decimal place.
Answer (Mean): _____________
b.
(4 Points) Find the sample mean and sample standard deviation for the percentage of Canadian Geese nests
which are successful. Round the standard deviation to one decimal place.
Answer (Mean): _____________
2.
Answer (Standard Deviation): _____________
Answer (Standard Deviation): _____________
The data shown below represents the annual salaries, in thousands of dollars, of a sample of five executives from
area businesses.
200,205,220,240,300
a.
(2 Points) Increasing each salary by $25,000 would do what to the mean? Explain in a brief sentence.
Answer:
b.
(2 Points) Increasing each salary by $25,000 would do what to the standard deviation? Explain in a brief
sentence.
Answer:
3.
The length of human pregnancies from conception to birth varies according to a distribution that is approximately
Normal with a mean of 266 days and a standard deviation of 16 days. Use the 68-95-99.7 rule to answer the
following questions.
a.
(2 Points) Almost all (99.7%) pregnancies fall in what range of lengths? (Use the 68-95-99.7 rule.)
Answer: _______________
b.
(2 Points) Approximately what percentage of pregnancies last less than 250 days? (Use the 68-95-99.7 rule.)
Answer: _______________
c.
(2 Points) Approximately what percentage of pregnancies last between 250 days and 298 days? (Use the 68-9599.7 rule.)
Answer: _______________
d.
(2 Points) Suppose that we randomly choose one recently pregnant mother from a large group of recently
pregnant women and asked her how long her pregnancy lasted. Would you be shocked if she said that is lasted
less than 218 days? Explain. (Use the 68-95-99.7 rule.)
Answer:
4.
th
(2 Points) The rules at an elite prep-school state that a student must score at or above the 80 percentile on the
math placement exam in order to be accepted into the school’s honor’s program. Timmy’s mother calls the school
and is furious. She says, “My son Timmy received a grade of 85% on the math placement exam and thus should be
enrolled in the school’s honor’s program!” She sarcastically follows this tirade with the remark, “You don’t need to
be a statistician to see that 85% is larger than 80%!”
Is her logic correct, and should Timmy be admitted into the program? Explain.
Answer:
5.
(2 Points) A college wide math placement exam has an approximate Normal distribution with a mean of 70 points
th
and a standard deviation of 6 points. Approximately what score represents the 84 percentile? Round your answer
to the nearest whole number.
Answer: _______________
6.
You are attending a local Star Trek convention and you are curious on the average number of times a Trekkie (i.e.
Star Trek fan) has seen the original Star Trek movie. You survey n = 256 individuals and compute the sample mean
number of viewings as x  45 viewings with a standard deviation of s = 20 viewings.
a.
(4 Points) Find both a 90% and a 99% confidence interval for the mean number of viewings of the original Star
Trek movie by a Trekkie. Round your values to the nearest whole number and give your answers in the form
of lower value to upper value.
90% Answer: ______________________
b.
99% Answer: ______________________
(2 Points) Suppose that you hypothesized that the actual mean number of viewings from all Trekkies (i.e. the
population’s parameter) was 38 viewings. Would the above found confidence intervals give support to your
hypothesis (YES or NO)? Explain.
Answer:
7.
(2 Points) The amount of time that it takes me to drive to UVM has a normal distribution with a mean of 18 minutes
and a standard deviation of 2.5 minutes. Approximately what percentage of my trips should take between 16 and
23 minutes? Give your answer as a percentage rounded to the nearest whole number.
Answer: _______________
8.
(2 Points) After extensive data collection, it is found that the average number of songs on an iPod is 1205 songs with
a standard deviation of 204 songs. The claim is made approximately 99.7% of iPods will have between 593 songs
and 1817 songs.
In order to make this claim, a crucial piece of information must be known about the distribution of the data.
What is this crucial piece of information?
Answer:
9.
You are working at a local casino and it is your job to test the six-sided dice at the Craps Table. A new shipment has
come in and you are not sure if the dice are weighted correctly…thus, the dice may not be fair. Suppose that you
toss a die in the air n = 400 times and it lands a ❹ on r = 100 of the tosses.
a.
(2 Points) Based on your data, give the 95% confidence interval for the proportion of tosses resulting in a ❹.
Give the interval in the form p̂  E where E is the margin of error and both values are given as percentages.
Also, round the margin of error to one decimal place.
Answer: ______________
b.
(2 Points) Do you think that the die is fair (YES or NO)? Explain.
Answer: