Normal Distribution - shows data that vary randomly from the mean
Normal Curve - bell-shaped curve
The Standard Bell Curve

Survey: How much time do you spend at meals in one week?
*Normally distributed with a mean of 13 hours, standard deviation of 3 hours.
1. Interval of data within 1 standard deviation of the mean?
2. What percent of the data can you expect to find between 10 hours and
16 hours?
3. Of 111 responses, how many could you expect to be between 16 and
19?

A college class of 174 students has an average final exam score of
68.5% and a standard deviation of 7.3%. The grade pattern follows a normal curve.
1. What percentage of students receive grades within two standard deviations of the mean?
2. How many students scored above a 68.5%?
3. About what percentage of students receive grades of 61.2% or below?

HW:
#9-27 odd
12.5#1-6, 9-11, 15-19, 22, 24
12.6 #8, 10, 15-20, 22

Normal Distributions
Lesson 12-7
Additional Examples
Algebra 2
Use the data from Example 1 to estimate the number of babies that are between 1.5 and 2.5 standard deviations from the mean birth weight.
The standard deviation in birth weights is about 500g.
Estimate and add the percents for 2000 –2499 and 4000–4499.
5% + 5% = 10%
About 10% of the babies are between 1.5 and 2.5 standard deviations from the mean birth weight.

Normal Distributions
Lesson 12-7
Additional Examples
Algebra 2
A survey of the employees of XYZ Corporation found that the mean of the morning commute times to work was 18 minutes. The standard deviation was 4 minutes. Sketch a normal curve showing the commute times at one, two, and three standard deviations from the mean.

Normal Distributions
Lesson 12-7
Additional Examples
Algebra 2
In a survey, the responses to the question, “How much time do you spend in the shower every day?” were normally distributed.
The mean was 15 minutes; the standard deviation was 2 minutes.
a.
What values are one deviation from the mean?
b.
What percent of the responses would you expect to find that are less than 13 and greater than 17?
Values that are one standard deviation from the mean have z -scores of –1 and 1.
value – mean z -score =
–1 = v
– 15 standard deviation
1 = u
– 15
2 2 v = 13 u = 17
The values 13 minutes and 17 minutes are one standard deviation from the mean.
The responses are normally distributed, and 13 and 17 are the values that are one standard deviation from the mean.
Since 68% of the data are within one standard deviation of the mean,
100% – 68% = 32% should be the values outside one standard deviation of the mean, i.e. values less than
13 and greater than 17.

Normal Distributions
Lesson 12-7
Additional Examples
Algebra 2
Use the distribution to answer the following questions.
Assume there are 92 students in the lecture class.
The professor has found that students who score between one and two standard deviations below the mean need to attend study sessions in order to pass the class. How many students need to attend study sessions?
Use the normal curve. About 13.5% of the students receive grades from one to two standard deviations below the mean.
Find the number of students that corresponds to 13.5%.
0.135(92) = 12.42
About 12 or 13 students need to attend study sessions.