Download Normal Distribution Distribution of data can be Uniform, Skewed or

Normal Distribution
Distribution of data can be Uniform, Skewed or Normal
Normal distribution takes the shape of a bell curve
68.3% of data lies within 1σ of mean
95.5% of data lies within 2σ of mean
99.7% of data lies within 3σ of mean
99.9% of data lies within 4σ of mean (all)
68%
95%
99%
Example 1 The average daily number of customers at a
clothing store is 150 customers with a standard
deviation of 18 customers. Sketch a normal curve that
represents the frequency of daily numbers of customers.
First, find the v
normal distribu
Then, sketch the
the horizontal s
Example 2 Refer to Example 1. Over a period of 200 days,
estimate how many days had customer totals in each of
the following intervals.
a. 132 - 168 customers
b. 114 - 186 customers
c. 96 - 204 customers
Open your book to page 919.
The tables give the fractional parts of a normally
distributed set of data for selected areas about the mean.
t = # of standard deviations (σ) from the mean
(above and below)
X ± tσ
P = fractional part of the data that lies in the interval.
The percent of the data within these limits is 100P
Example 3 Find the upper and lower limits of an interval
about the mean within which 52% of the values of a set
of normally distributed data can be found if X = 92
and s = 7.
Example 4 The test scores for students who have taken a
language arts proficiency exam follow a normal
distribution with a mean of 72. The lowest score is 44
and the highest score is 100.
a. Determine the standard deviation.
b. What percent of the students taking the test
would score between 56 and 88?
Example 5 The class of 1996 was the first to take the
adjusted SAT. It was adjusted so that the median of the
scores for the verbal section and the math section would be
500. For each section, the lowest score is 200 and the
highest score is 800. Suppose the verbal and math scores
follow the normal distribution.
a. Determine the standard deviation.
b. What percent of the students taking the test
would have a math score between 375 and 625?
c. What is the probability that a senior chosen has
a math score between 550 and 650?