Transcript Ex: Daily Rainfall, Height, Time

Section
6.1
Graphs of Normal
Probability Distributions
Recall:
Continuous Random Variable: outcomes you measure, not
count.
Ex: Daily Rainfall, Height, Time
The normal distribution is most widely used for
continuous RVs.
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Properties of the Normal Curve
1. Data is bell-shaped, highest point over µ
2. Controlled by µ and σ
3. µ is the balancing point and σ determines the spread
4. Area under the curve totals 1
Note: if  is large, the curve will be more spread out;
if it is small, the curve will be more peaked.
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Structure of Normal Curve
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Empirical Rule
if the data is normal…
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Ex: 1
Playing life of a Sunshine radio is normally distributed w/
 = 600 hours and  = 100 hours.
What is the probability that a radio selected at random will
last from 600 to 700 hours?
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Ex: 2
a) Do these distributions have the same mean?
b) One curve has σ = 3 and the other σ = 1. Which is
which?
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Ex: 3
The yearly wheat yield per acre on a farm is normal with
µ = 35 bushels and σ = 8 bushels.
a) Sketch the Empirical Rule:
b) What is the probability that the yield will be between 19
and 35 bushels?
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Control Charts
1. When examining data over a period of equally spaced
time intervals or in some sequential order
2. It’s a warning device to inspect variability and identify
statistical control or out-of-control in production over
time
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Steps to make a control chart
1. Identify µ and σ
2. Mark µ (solid line), 2σ, 3σ (dashed lines) values on
the y-axis
3. Mark time sequence on the x-axis
4. Plot the data in order and connect the dots
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Ex: 4
Every summer Ms. Tamara hires many part-time
employees at her lodge. One of the biggest activities for the
lodge staff is that of “making up” the rooms each day.
Although the rooms are supposed to be ready by 3:30
P.M., there are always some rooms not made up by this
time because of high personnel turnover. Based on past
experience, rooms not made up by 3:30 P.M. is
approximately normal, with mean  = 19.3 rooms and
standard deviation  = 4.7 rooms.
For the past 15 days, the housekeeping unit has
reported the number of rooms not ready by 3:30 P.M.
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Ex: 4 – Solution
Number of Rooms Not Made Up by 3:30 P.M.
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Two more reports
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Section 6.1 Assignment:
Pg.281: #(1-15) Odd
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