lecture 10.4 b bt
TRANSCRIPT
Today’s Agenda
Attendance / Announcements
Sections 10.4b
Have a good Holiday!
Exam Schedule
Exam 5 (Ch 10)
Thur 12/5
Final Exam (All)
Thur 12/12 1 hour, 50 mins
The Normal Curve
The Normal Curve
The Normal Curve
The Normal Curve
The Normal Curve
Z-scores:
The Normal Curve
The following are synonymous
when it comes to the normal curve:
• Find the area under the curve …
• Find the percentage of the population
…
• Find the probability that …
The Normal Curve
Using a Z-Table to find probabilitiesNote: Our Z-table only gives area to the left
(or probabilities less than z)
The Normal CurveFind Probability that
z < 0.97
Z-scores: -2 -1 0 1 2 3-3
0.97
Find area under the
curve to the left of
z = 0.97)97.0(zP
Using a Z-Table to find probabilitiesFind Probability that
z < 0.97
Since z > 0, use
positive side
The Normal CurveFind Probability that
z < -2.91
Z-scores: -2 -1 0 1 2 3-3
-2.91
Find area under the
curve to the left of
z = -2.91
Using a Z-Table to find probabilitiesFind Probability that
z < -2.91
Since z < 0, use
negative side
Using a Z-Table to find probabilities
• Not all Z-Tables are alike!
Using a Z-Table to find probabilities
• But we can still use our z-table to
find areas to the right (probability
greater than), as well as areas
between two values (probability
between two values).
The Normal CurveFind Probability that
z > 0.75
Z-scores: -2 -1 0 1 2 3-3
0.75
Find area under the
curve to the right of
z = 0.75
Finding Area to the Right
• Two Methods
–Using the Complement of 1
–Using Symmetry
Complement MethodFind Probability that
z > 0.75
Z-scores: -2 -1 0 1 2 3-3
0.75
Find area under the
curve to the right of
z = 0.75
Complement MethodUse fact that area
under entire curve is 1.
And that we can find
area to the left
Z-scores: -2 -1 0 1 2 3-3
0.75
Find area under the
curve to the right of
z = 0.75
Complement MethodUse fact that area
under entire curve is 1.
And that we can find
area to the left
Z-scores: -2 -1 0 1 2 3-3
0.75
Find area under the
curve to the right of
z = 0.75
The Normal CurveFind Probability that
z > 0.75
Z-scores: -2 -1 0 1 2 3-3
0.75
Find area under the
curve to the right of
z = 0.75
Symmetry Method
Symmetry MethodUse symmetry of the
normal curve to find
area
Z-scores: -2 -1 0 1 2 3-3
0.75
Find area under the
curve to the right of
z = 0.75
- 0.75
Finding Area between two values
• Just use difference of the two
areas
Difference of AreaFind Probability that
-1.25 < z < 0.75
Z-scores: -2 -1 0 1 2 3-3
0.75
Find area under the
curve between -1.25
and 0.75
-1.25
Finding Probabilities of Normal Distributions
1. For data that is normally distributed, find the percentage of data items that are:
a) below z = 0.6b) above z = –1.8c) between z = –2 and –0.5
Finding Probabilities of Normal Distributions
2. Given a data set that is normally distributed, find the following probabilities:
a) P(0.32 ≤ z ≤ 3.18)b) P(z ≥ 0.98)
Solving Applications of Normal Distributions
Before solving real world applications of data that is normally distributed, we need to first calculate any appropriate z-scores based on the data. This is called normalizing the data.
Solving Applications of Normal Distributions
Systolic blood pressure readings are normally distributed with a mean of 121 and a standard deviation of 15. After converting each reading to its z-score, find the percentage of people with the following blood pressure readings:
a) below 142b) above 130c)between 142 and 154
Solving Applications of Normal Distributions
A machine produces bolts with an average diameter of 7 mm and a standard deviation of 0.25 mm. What is the probability that a bolt will have a diameter greater than 7.1 mm? Assume the distribution is normal.
Solving Applications of Normal Distributions
The placement test for a college has scores that are normally distributed with = 500 and = 100. If the college accepts only the top 10% of examinees, what is the cutoff score on the test for admission? (hint: you’ll need to use the table first, and work backwards)
Classwork / Homework
• 10.4 Worksheet
• Page 638
•1 – 4, 9 – 19 odd, 25 – 35 odd