WARM UP:
 If E and F are two independent events with P(E)=.2 and
P(F)=.4 find:




1)
2)
3)
4)
P(E|F)
P(F|E)
P(E∩F)
P(EUF)
 1) .2
2. .4
3) .08
3) .52
9.6 THE NORMAL
DISTRIBUTION
SWBAT compute
a z-score, use
the standard
normal cur ve,
and approximate
the binomial
distribution.
PROPERTIES OF NORMAL DISTRIBUTION:
Bell shaped and symmetric with respect to mean.
Mean, median and mode are equal.
Area enclosed by x-axis and curve’s = 1sq unit.
Probability that an outcome of a normally distributed curve is
between b and a equals the area associated w the curve from
x=a to x = b.
 Standard deviation plays a major role in describing the area
under the curve.




STANDARD DEVIATION RELATED TO AREA
UNDER A NORMAL CURVE:
34.135%
34.135%
13.59%
13.59%
2.14%
µ-3σ
µ-2σ
µ-σ
µ
2.14%
µ+σ µ+2σ µ+3σ
Z-SCORE: (A GROUP MEAN)
𝑍=
𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑥 𝑎𝑛𝑑 𝜇
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
=
𝑥−𝜇
𝜎
Where
x = Original Data Point
µ = Mean of Original Data
σ = Standard Deviation of Original Data
Z- score transforms any normal value with a mean m
and standard deviation s to a normal value with
mean 0 and standard deviation 1.
ON A TEST, 80 IS THE MEAN AND 6 IS THE
STANDARD DEVIATION.
 What is the Z-Score of a score of 89?
𝑍=
𝑥−𝜇 89−80
=
𝜎
6
= 1.5
FIND THE AREA, THAT IS FIND THE
PROPORTION OF CASES INCLUDED BET WEEN
THE GIVEN VALUES:
0
 See the Z-Score Table.
1.2
1.94
FIND T WO VALUES: SCORE AT 1.2 AND THE
SCORE AT 1.94.
 At 1 .2: 0.3849
 At 1 .94: 0.4738
 So we will subtract the two since .3849 is the area from 0 to
1 .2 and .4738 is the area from 0 to 1 .94.
 .4738 - .3849 = .0889
SCORES ON A TEST ARE NORMALLY DISTRIBUTED
WITH A MEAN OF 75 AND A STANDARD DEVIATION OF
8. WHAT IS THE PROBABILIT Y THAT A TEST CHOSEN
AT RANDOM IS BET WEEN 80 AND 90?
 Find area under a normal curve from x1 = 80 and x2 = 90. So
find Z scores for both:
80 − 75
𝑍1 =
= .625
8
90 − 75
𝑍2 =
= 1.875
8
*Now go to the table and subtract to find the probability….or the
area between:
.4699 - .2357 = .2342 = 23.42%
*Note: Round to nearest 100 th w three decimal places.
HW WS 9.6: 1,3, 5A -C, 7A-C, 9,11,13, 15A -C,
19
*Keep your Z- score chart to use on your test!!