Normal
Distributions
Ch. 6 Day 1
AP Statistics
EQ: What happens when we alter data sets in terms
of the measures of center and spread? What is the
normal distribution and why do we use it?
What happens when we…?
Add or subtract a constant
to each data value?
Multiply or divide a
constant to each data
value?
Normal Distribution Uses
1. Good for real data
2. Good approximations to the results of
chance outcomes
3. Many statistical inference procedures based
on normal distributions work well for other
roughly symmetric distributions
Z-Scores
• Formula (on your sheet!!!!!!!)
• Purpose-to express the distributions in a
common scale.
• They tell us how many standard deviations the
observation is from the mean and in which
direction.
• Standardizing into z-scores does
not change the shape of the
distribution.
• It does change the center to 0
and the spread to a standard
deviation of 1.
• Draw a picture
• Show all work neatly!
• Get the correct answer
• Write a sentence that answers
the question.
Use the z-table to find:
P(z < 1.2)
P(z > 2.47)
P(-1.4 < z < 2.71)
The weights of cockroaches living in a typical college
dormitory are approximately normally distributed
with a mean of 80 grams and a standard deviation of
4 grams. The percentage of cockroaches weighing
between 77 and 83 grams is about:
A) 99.7% B) 95%
C) 68%
D) 55%
E) 34%
On the driving range, Tiger Woods
practices his swing with a
particular club by hitting many,
many balls. When Tiger hits his
driver, the distance the ball
travels follows a normal
distribution with mean 304 yards
and standard deviation 8 yards.
A. What percent of Tiger’s drives travel at least
290 yards?
B. What percent of Tiger’s drives travel between
305 yards and 325 yards?
C. What distance would a ball have to travel to be
at the 80th percentile of Tiger Woods’s drive
lengths?
High levels of cholesterol in the blood increase
the risk of heart disease. For 14 year old boys,
the distribution of blood cholesterol is
approximately normal with mean 170 mg of
cholesterol per deciliter of blood and standard
deviation 30 mg/dl. What is the IQR of the
distribution of blood cholesterol?
Maple tree diameters in a forest area are
normally distributed with mean 10 inches and
standard deviation 2.2 inches. Find the
proportion of trees having a diameter greater
than 15 inches.
The Graduate Record Examination (GRE) is widely
used to help predict the performance of applicants
to graduate school. The range of possible GRE sores
is 200 to 900. The math dept. at a university finds
that the sores of its applicants on the verbal portion
of the GRE are approximately normal with mean of
612 and a standard deviation of 103. To be accepted
into a graduate program at this university, a student
must sore in the top 25% of the GRE. What score
must a student get to be accepted?
Homework (Practice)
P. 129 # 1, 2, 7, 9, 12, 44, 45