Assignment 5 STAT 2023 spring 2016
1. The Empirical Rule. Go to https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule
Read the top section of the above webpage. Summarize the information in your own words in
at least 3 sentences.
2. 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.
Read the top two sections of the above webpage. Summarize in your own words each section.
State at least 2 sentences to summarize each section
a.
Section One:
b.
Section Two:
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.
c. What is the approximate percent of the area between 51 and 61?
d. What is the approximate percent of the area below 53.5?
e. What is the approximate percent of the area above 61?
f. What is the approximate percent of the area between 58.5 and 63.5?
g. What is the z-score for 63.3?
h. What is the z-score for 61?
i. What is the data value associated with the z-score of -1.5?
j. 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. 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 nonreproducing 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 1.25? Round to 1 digit past decimal.