MARIO F' TRIOLA

1
STATISTICS
ELEMENTARY
Section 5-3 Normal Distributions Finding
Probabilities
MARIO F. TRIOLA
EIGHTH
EDITION
2
Other Normal Distributions

• If ? ? 0 or ???? 1 (or both), we could convert
  values to standard scores (z scores) using the
  formula
• Then we could use the procedures for working with
  the standard normal distribution.
• But . . . we can also use the TI-83 directly by
  specifying the mean and standard deviation as
  follows
• normalcdf(lower, upper, mean, sd)

3
Probability of Weight between 143 pounds and 201
pounds
There is a 0.4772 probability of randomly
selecting a woman with a weight between 143 and
201 lbs.
OR 47.72 of women have weights between 143 lb
and 201 lb.
µ 143
s ????29
Weight
143 201
Figure 5-14
4
STATISTICS
ELEMENTARY
Section 5-4 Normal Distributions Finding
Values
MARIO F. TRIOLA
EIGHTH
EDITION
5
Cautions to keep in mind

• 1. Dont confuse z scores and areas.
•     Z scores are distances along the horizontal
   scale, but areas are regions under the  normal
  curve.
• 2. Dont confuse probabilities with data
  values.
• Given values, find probabilities
• use normalcdf.
• Given probabilities, find values
• use invnorm.

6
Finding z Scores when Given Probabilities
95
5
1.645
0
FIGURE 5-11 Finding the 95th Percentile
7
Finding z Scores when Given Probabilities
90
10
-1.28
0
FIGURE 5-12 Finding the 10th Percentile
8
Finding a value when given a probabilityusing
the TI-83

• Draw a normal curve,
• draw the centerline,
• shade the region under the curve
• that corresponds to the given probability, and
• enter the probability value in the region.
• If the area shaded is not to the left of the
  desired value desired, subtract the probability
  from 1 to find the area to the left of the
  desired value.
• Press 2nd DISTR,
• select 3invNorm(,
• type area, mean, sd and press enter.

9
Finding P10 for Weights of Women
90
10
µ 143
s ????29
Weight
143
x
106
The weight of 106 lb (rounded) separates the
lowest 10 from the highest 90.
FIGURE 5-17