# Unit 4 The Normal Curve and Normal Approximation FPP Chapter 5 - PowerPoint PPT Presentation

PPT – Unit 4 The Normal Curve and Normal Approximation FPP Chapter 5 PowerPoint presentation | free to download - id: 17e10e-ZDc1Z

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## Unit 4 The Normal Curve and Normal Approximation FPP Chapter 5

Description:

### For many lists, the % entries falling into an interval can be estimated using the normal curve. ... Some Normal Curve Problems ... – PowerPoint PPT presentation

Number of Views:168
Avg rating:3.0/5.0
Slides: 18
Provided by: NRC2
Category:
Transcript and Presenter's Notes

Title: Unit 4 The Normal Curve and Normal Approximation FPP Chapter 5

1
Unit 4The Normal Curve and Normal
ApproximationFPP Chapter 5
0.4
0.3
0.2
0.1
0.0
-4
-3
-2
-1
0
1
2
3
4
X
• 2. Area under the curve 100
• 3. Always above the horizontal axis
• 4. Area between -1 and 1 is about 68.
• Area between -2 and 2 is about 95.

A.05
2

-30
-20
-10
0
10
20
30
X
50
40
60
20
10
30
70
0
80
X
Standard units say how many SDs above or below
the average a value is. They allow us to compare
different normal curves.
3
Normal Approximation
For many lists, the entries falling into an
interval can be estimated using the normal
curve. (1) Convert the interval in question to
standard units. (2) Find the area above this
interval, under the normal curve. That area is
approximately the entries from the list falling
into the interval.
0.4
0.3
0.2
0.1
0.0
? ? ? ? ? ? ? ? ? Original
Units
Standard Units
-4
-3
-2
-1
0
1
2
3
4
4
Example Exam Scores
• Average score 20 points SD 5 points
• You score 25 points.
• Is your score above or below average?
• How many points above or below average?
• How many SDs is that?
• 25 points is ___________ in standard units.
• Convert the score points to standard
units.
• What is the score 20 points in standard units?

5
6
(No Transcript)
7
Normal Curve Arithmetic
8
Normal Curve Arithmetic
9
Service Times
• The time to complete the 40,000 mile service at a
local automobile dealership follows a normal
curve with average 100 minutes and SD 10 minutes.
• What is the probability that it will take between
100 and 115 minutes?
• You bring your car in for service, but you need
it to be done in 120 minutes or less. What is
minutes or less?

10
Percentiles
• Refer back to the Exam Scores example
• What is the 90th percentile?
• What is the 10th percentile?

11
Some Normal Curve Problems
• 1. The diameters of metal rods manufactured by a
certain supplier follow a normal distribution
with mean 4.0 centimeters and SD 0.2 centimeters.
• (a) What proportion of the rods have diameters
less than 3.8 cm?
• (b) What proportion of the rods have diameters
greater than 4.2 cm?
• (c) What proportion of the rods have diameters
between 3.9 and 4.1 cm?
• 2. A consultant states that her uncertainty
about the time needed to complete a construction
project can be represented by a normal random
variable with mean 60 weeks and SD 8 weeks.
• (a) What is the probability that the project
will take more than 70 weeks to complete?
• (b) What is the probability that the project
will take less than 52 weeks to complete?
• (c) What is the probability that the project
will take between 52 and 70 weeks to complete?

12
More Normal Curve Problems
• 3. A company services gas central-heating
furnaces. A review of its records indicates that
the time taken for a routine maintenance service
call can be represented by a normal distribution
with mean 60 minutes and SD 10 minutes.
• (a) What proportion of such service calls take
more than 45 minutes?
• (b) What proportion of such service calls take
less than 75 minutes?
• (c) Sketch a graph to illustrate the reason for
the coincidence in the answers to (a) and (b).
• 4. On average, graduates of a particular
university earn 59,000 five years after
graduation. The standard deviation is 4,000.
What percent earn less than 54,000? What
percent earn more than 70,000? What assumptions
did you make? Are those assumptions reasonable?

13
Even More Practice Problems
• 5. Trucks at a certain warehouse are loaded with
200 boxes each. It is known that, on average, 8
percent of the time do 21 or more boxes get
damaged if the SD is 3.8 boxes? What assumptions
did you make?
• 6. I am considering two alternative investments.
In both cases, I am unsure about the percentage
return but believe that my uncertainty can be
represented by normal distributions with means
and SD's as follows. For Investment A, the mean
is 10.4, the SD is 1.2. For Investment B, the
mean is 11.0, the SD is 4.0. I want to make the
investment that is more likely to produce a
return of at least 10.
• Which should I choose?

14
More Practice Problems
• The mean GPA of University of Washington's last
graduating class was 2.7 with SD 0.4. What GPA
did the 90th percentile have?
• 8. In a 3 year period, 665,281 people took the
GMAT (including repeaters). The distribution of
scores approximately follows a normal curve. The
mean score was 492 and the SD was 103. What was
the 80th percentile for these GMAT scores? What
proportion of scores were above 550?

15
More Normal Curve Problems
• 9. It is estimated that major league baseball
game times to completion follow a normal
distribution with mean 132 minutes and SD 12
minutes.
• (a) What proportion of all games last between
120 and 150 minutes?
• (b) Thirty-three percent of all games last
longer than how many minutes?
• (c) What is the 67th percentile of game times to
completion?
• (d) What proportion of games last less than 120
minutes?
• 10. The weights of the contents of boxes of a
brand of cereal have a normal distribution with
mean 24 ounces and SD 0.7 ounces.
• (a) What is the probability that the contents of
a randomly chosen box weigh less than 23 ounces?
• (b) The contents of 10 of all boxes weight more
than how many ounces?
• (c) What proportion of boxes have contents
weighing between 23.5 and 24.5 ounces?

16
• 11. A management consultant found that the amount
of time per day spent by executives performing
tasks that could be done equally well by
subordinates followed a normal distribution with
mean 2.4 hours. It was also found that 10 of
executives spent over 3.5 hours per day on such
tasks. Find the standard deviation of the
distribution of daily time spent by executives on
• 12. The cereal manufacturer of problem 10 wants
to adjust the production process so that the mean
weight of the contents of the boxes of cereal is
still 24 ounces, but only 3 of the boxes will
contain less than 23 ounces of cereal. What SD
for the weights of the contents is needed to
attain this objective?

17
• 13. A video display tube for computer graphics
terminals has a fine mesh screen behind the
viewing surface. During assembly the mesh is
stretched and welded onto a metal frame. Too
little tension at this stage will cause wrinkles,
while too much tension will tear the mesh. The
tension is measured by an electrical device with
output readings in millivolts (mV). At the
present time, the tension readings for successive
tubes follows a normal distribution with mean 275
and standard deviation 43 mV.
• (a) The minimum acceptable tension corresponds
to a reading of 200 mV. What proportion of the
tubes exceed this limit?
• (b) The mean tension can be adjusted in the
production process, but the SD remains at 43 mV
regardless of the mean tension setting. What
mean tension setting should be used to make it so
that 2 of the tubes have tension readings below
the limit of 200 mV?
• (c) In production, tension above 375 mV will
usually tear the mesh. Thus the acceptable range
of tension readings is actually 200 mV to 375
mV. What proportion of tubes are in this
acceptable range?