Download 6.2 Introduction to the Standard Normal Curve

6.2 Introduction to the Standard Normal Curve
Upon completion of the tihs activity and any associated homework, you should
be able to:
• Graph a normal curve and summarize its important properties
• Apply the empirical rule (a.k.a. the standard deviation rule, a.d.a. the
68–95–99.7 rule) to the special case of distributions having the normal
shape
1. The scores on a statistics exam were approximately normal with mean
78 and standard deviation 7. Below is a generic Normal Distribution.
Mark and label the location of the mean and one, two, and three standard
deviations above and below the mean.
(a) Utilizing the Empirical Rule, indicate the middle 68%, 95%, and
99.7% of the graph.
(b) What percent of the students scored between a 71 and 85? Set up
and use the probability density curve below to shade the area you
used to answer the question (this is how you show your work).
(c) What is the range of scores for the lowest 16% of the class? Set up
and use the probability density curve below to shade in the area you
used to answer the question (this is how you show your work).
(d) What percent of the class scored higher than 85? Set up and use
the probability density curve below to shade in the are you used to
answer the question (this is how you show your work).
2. The length of human pregnancies from conception to birth varies according
to a distribution that is approximately normal with a mean of 266 days
and a standard deviation of 16 days.
(a) Use the drawing of the normal density curve below to mark and label
the location of the mean and one, two, and three standard deviations
above and below the mean.
(b) What percent of the pregnancies last between 250 and 282 days?
Show your work.
(c) What are the upper and lower bounds for the middle 95% of all
pregnancy lengths. Be sure to show your work.
(d) What percent of the pregnancies last between 218 and 314 days? As
always, be sure to use the density curve to show your work.
(e) What percent of the pregnancies last 266 days or fewer?
(f) What percent of the pregnancies last between 266 and 282 days?
(g) What percent of the pregnancies last fewer than 250 days?
(h) What percent of the pregnancies last between 234 and 314 days?
(i) How long are the longest 2.5% of pregnancies?
3. These data were collected by polling middle and high school students in
the Pittsburg (CA) Are about drug use (SOURCE: Los Medanos College
Path 2 Stats program).
±1 Standard Deviation Hat Plot
10.1
12.15
14.2
A 30
25
20
15
10
5
0
6
7
8
9
10 11 12 13 14 15 16 17
Age Started Recreational Drug Use
(a) Is the distribution approximately normal? Why or why not?
(b) What is one standard deviation? Explain how you found the standard
deviation.
(c) At what ages did the middle 68% of students begin recreational drug
use?
(d) What are the boundaries for the typical range of students?
(e) What is the maximum age of the youngest 16% of students to begin
recreational drug use?
(f) What is the minimum age of the oldest 50% of students to begin
recreational drug use?
(g) What percent of students were age 16.25 years or older when they
began recreational drug use?