Page 857 - Algebra 1

Some data is said to be normally distributed. The shape of the data looks like a bell, so it is often called a “bell-shaped curve.” The mean is at the center.
68%
-3SD -2SD -1SD mean +1SD +2SD +3SD
As the graph indicates, 68% of the data falls within one standard deviation of the mean. 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.
Using the Normal Distribution
The ages of people at a park are normally distributed. The mean is 18 years and the standard deviation is 6 years. Between what two ages do 95% of the ages fall?
SOULTION
Because it is a normal distribution, 95% of the data falls within 2 standard deviations of the mean.
18 ± 2(6) = 18 ± 12 95% of the ages fall between 6 and 30.
Find the standard deviation of the data.
(Ex 1)
a. An ATM machine records the values of the withdrawals made in one day. {20, 100, 20, 200, 20, 20, 100, 20, 80, 20, 20, 40, 100, 40, 100}
b. A group of students is asked how many movies they watched in the last month. Their responses are recorded in the data set.
{4, 10, 6, 8, 4, 5, 30, 4, 2, 3, 1}
Find the mean and standard deviation of the data. Identify any outliers, and if one is found, explain how it affects the mean.
95%
99.7%
Example
3
Lesson Practice
c.
(Ex 2)
d.
(Ex 1)
e.
(Ex 3)
f.
(Ex 3)
Twelve students are asked how many books they read last year. Their responses are recorded in the data set.
{12, 15, 30, 14, 13, 9, 10, 10, 11, 12, 14, 8} A teacher records the scores on a test.
{90, 95, 90, 85, 80, 80, 90, 40, 95, 90, 85, 90, 95, 80, 100}
Test Results The results on a test are normally distributed with a mean of 85 and a standard deviation of 5. Between what two scores are 68% of the scores?
Salaries The salaries of educators are normally distributed with a mean of $35,000 and a standard deviation of $10,000. Between what two scores are 99.7% of the salaries?
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Saxon Algebra 1