Download The 68-95-99.7 Rule (also called the EMPIRICAL RULE

The 68-95-99.7 Rule (also called the EMPIRICAL RULE):
A Normal distribution is a
collection of many data points
that form a bell shaped curve.
Note:
x = mean
s.d. = standard deviation

Approximately __________ of the observations fall within _______________ of the mean _____.

Approximately __________ of the observations fall within _______________ of the mean _____.

Approximately __________ of the observations fall within _______________ of the mean _____.
1. Determine the percentages of data of the standard Normal curve between each value:
a. Between mean ( x ) and 1 standard deviation:
b. Between +1 standard deviation and +2 standard deviation:
c. Between -3 standard deviation and –1 standard deviation:
2. The heights of students are approximately normal with a mean of 66” and a standard deviation of 3”.
Label the Normal curve:
What conclusions can you draw about the heights of the students?
1. ________________________________________________________________________________________________
2. ________________________________________________________________________________________________
3. ________________________________________________________________________________________________
Maria’s spelling bee scores follow a Normal distribution with a mean of 83 points and a standard deviation of 10.6 points.
(a) What are the values of Maria’s selling bee scores that are 1 standard deviation from the mean?
(b) What are the values of Maria’s selling bee scores that are 2 standard deviations from the mean?
(c) What are the values of Maria’s selling bee scores that are 3 standard deviations from the mean?
(d) What percent of the spelling bee scores fall between _____ and _____? (answers from part a)
(e) What percent of the spelling bee scores fall between _____ and _____? (answers from part b)
(f) What percent of the spelling bee scores fall between _____ and _____? (answers from part c)
Label the Normal curves for Maria
and
Heidi:
Heidi’s spelling bee scores follow a Normal distribution with a mean of 83 points and a standard deviation of 16.8 points.
(a) What are the values of Heidi’s selling bee scores that are 1 standard deviation from the mean?
(b) What are the values of Heidi’s selling bee scores that are 2 standard deviations from the mean?
(c) What are the values of Heidi’s selling bee scores that are 3 standard deviations from the mean?
(d) What percent of the spelling bee scores fall between _____ and _____? (answers from part a)
(e) What percent of the spelling bee scores fall between _____ and _____? (answers from part b)
(f) What percent of the spelling bee scores fall between _____ and _____? (answers from part c)
ADD THE DOT PLOTS ONTO THE NORMAL CURVES FOR MARIA & HEIDI’S SCORES.