STA 205 Pre-work for Group Assignment 1: Normal DistributionsDirections: Fully attempt all questions/parts by writing your answers and all supporting work on a separate
piece of paper. Be sure your work is clearly written and organized, labeling each question number and part.
Writing in pencil is recommended so that you are able to make edits when you meet with your group. Some
parts of the assignment are intentionally missing. These parts will be provided later and will be completed
with your group. Leave space on your paper for these questions. Take photos or scan your work and save it as
a single PDF file. Post your pre-work on your group’s discussion board before your group meeting time. (You
must have all questions fully attempted in your first post on the discussion board to receive any credit for the
1. The number of students per elementary school in the United States is approximately normally distributed
with a mean of 473.25 students and a standard deviation of 86.26 students. Use the Empirical Rule to
answer parts a – c. Use normal distributions to answer parts d – g. Round all z-scores to two decimal
places. Round all other answers to four decimal places.
a. Draw and label the normal model which describes the number of students per elementary school in
the United States.
b. What percentage of elementary schools in the US have between 386.99 and 559.51 students?
c. What percentage of elementary schools in the US have more than 645.77 students?
d. The elementary school that Dr. Lemmon’s children attend has 677 students. What percentage of
elementary schools have less than this many students?
e. How many students do the top 22% of elementary schools in the US have?
f. What percentage of elementary schools in the US have between 400 and 500 students?
g. How many students do the bottom 10% of elementary schools in the US have?
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