Assignment 3 STAT 2023 fall 2015
Part One:
The reading and the writing part:
The Empirical Rule. Go to https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule .
1. Read the top section of the above webpage. Summaries in your own words in 5 sentences or
more the information presented there.
2. Provide a screen shot or a snipping of the graph shown in the upper right of this webpage.
Z-Scores or Standardization of data values. Go to https://en.wikipedia.org/wiki/Standard_score .
Notice the word, DATUM, in the above reference. That means a single data point.
1. Read the top two sections of the above webpage. Summarize in your own words each section.
State at least three sentences to summarize each section
a. Section One:
b. Section Two:
2. Click on the graph in the upper right corner of this webpage. Based on the enlarged graph
answer the following questions.
a. What percent of the probably lies between z-scores of -1 and 1? State your answer as
number.
b. What percent of the probably lies between z-scores of -2 and 2? State your answer as
number.
c. What percent of the probably lies between z-scores of -3 and 3? State your answer as
number.
Part Two:
The calculation part:
3. Assume there is a mound shaped distribution with a mean of 56 and a standard deviation of 2.5.
Use this information to answer the following questions.
a. What is the approximate percent of the area between 51 and 61?
b. What is the approximate percent of the area below 53.5?
c. What is the approximate percent of the area above 61?
d. What is the approximate percent of the area between 58.5 and 63.5?
e. What is the z-score for 63.3?
f. What is the z-score for 61?
g. What is the data value associated with the z-score of -1.5?
h. What is the data value associated with the z-score of 2.2?
4. The former President of Oklahoma State University, David J. Schmidly, wrote a book
titled, The Bats of Texas. A type of bat described in the book is the Ghost-faced Bat.
This is a cave dwelling bat and the non-reproducing females live in interior cave
chambers that have an average temperature of 92.4F with a standard deviation of 0.45F.
Use this information to answer the remainder of the questions on this page. This
problem set is similar to our in class exercise on Lesson 5, but it has different numbers.
For each of these questions please state the answer.
a. What is the numerical interval that describes the set of non-reproducing female
interior cave chamber temperatures that are within one standard deviation of the
mean?
b. Assuming that the temperature of non-reproducing female interior cave chambers
has a mound-shaped distribution, then only approximately 2.5% of the time the
interior cave chamber temperature exceed what value?
c. State the value of the 84th percentile for the variable non-reproducing female interior
cave chamber temperature, assuming that the temperature of the non-reproducing
female interior cave chambers has a mound-shaped distribution.
d. Assuming that the temperature of non-reproducing female interior cave chambers
has a mound-shaped distribution, then one could conclude that approximately 100%
of the non-reproducing female interior cave chambers temperatures are between
what two values?
e. If nothing is known about the shape of the distribution of the temperature of nonreproducing female interior cave chambers, then one could conclude that at most
25% of the temperatures exceeded what value?
f. What is the z-score associated with the non-reproducing female interior cave
chamber temperature of 91.59?
g. What is the temperature of a specific non-reproducing female interior cave chamber
if it is associated with a z-score of 1.45? Round to 1 digit past decimal.