WARM UP
 An
unbiased coin is tossed 6 times. Our goal when
tossing a coin is to get heads.
 Calculate:
1.
At least 3 heads
2.
At most 2 heads.
MORE EXAMPLES FOR AREA
 Find
the area/probability of the following:
 Left of z = -2.50
P(z < -2.5)

Right of z = - 1.20
P(z > -1.2)
EVEN MORE EXAMPLES FOR AREA
 Find
the area/probability of the following:

P(0 < z < 2.32)

P(-1.2 < z < 2.3)
AND ONE MORE EXAMPLE FOR AREA
 Find

the area/probability of the following:
P(z < -3.01 and z > 2.43)
APPLICATION 1
A
Calculus exam is given to 500 students. The
scores have a normal distribution with a mean
of 78 and a standard deviation of 5. What
percent of the students have scores between
82 and 90? How many students have scores
between 82 and 90?
APPLICATION 2
A
Calculus exam is given to 500 students. The
scores have a normal distribution with a mean
of 78 and a standard deviation of 5. What
percent of the students have scores above
70? How many students scored above a 70?
APPLICATION 3
 Find
the probability of scoring below a 1400
on the SAT if the scores are normal
distributed with a mean of 1500 and a
standard deviation of 200.
FINDING Z-SCORES FROM AREA
 Find
the z-score above the mean with an area
to the left of z equal to 0.9325
 Find
the z-score below the mean with an area
to the left of z equal to 13.87%
WARM-UP
1. Find the percentage of the given z-score.
a) z is less than -0.47
b) z is greater than 0.54
c) z is less than 2.03
d) z is greater than 1.16
2. Find the percentage of the given z-score.
a) Z is between -2.05 and 0.78
b) z is between -1.11 an -0.32
MORE FINDING Z-SCORES FROM AREA
 Find
the z-score below the mean with an area
between 0 and z equal to 0.4066
EVEN MORE FINDING Z-SCORES FROM AREA
 Find
the z-score above the mean with an area
between 0 and z equal to 0.2123
 Find
the z to the right of the mean with an
area to the right of z equal to 0.0239
INVERSE NORMAL DISTRIBUTIONS

Find k for which P(x < k) = 0.95 given that x is normally
distributed with a mean of 70 and a standard deviation of
10.
SKIP

APPLICATIONS

A professor determines that 80% of this year’s History
candidates should pass the final exam. The results are
expected to be normally distributed with a mean of 62 and
standard deviation of 13. Find the lowest score necessary to
pass the exam.
MORE APPLICATIONS

Researchers want to select people in the middle 60% of the
population based on their blood pressure. If the mean is 120
and the S.D. is 8. Find the upper and lower reading that
would qualify.
FINDING STATS BASED ON PROBABILITY

Sacks of potatoes with a mean weight of 5 kg are packed by
an automatic loader. In a test, it was found that 10% of bags
were over 5.2 kg. Use this information to find the standard
deviation of the process
MORE FINDING STATS BASED ON
PROBABILITY

Find the mean and the standard deviation of a normally
distributed random variables X, if P(x > 50) = 0.2 and P(x <
20) = 0.3
SKIP

MEASURING LOCATION IN A DISTRIBUTION

Draw a dotplot for class data, displaying the height of students in
a class.
The
pth percentile of a distribution is
the value with p percent of the
observations less than or equal to it.
 Percentiles
separate data sets into 100
equal parts. The percentile rank of a data
value is the percentage of data values that
are less than or equal to that value.
1. For Brett, who is 74 inches tall, find
his percentile rank?
2. For Ms. Watts, who is 69 inches tall,
find her percentile rank?
3. When the heights of 250 9th grade boys were measured,
Jaden found that his height placed him at the 82nd percentile.
Which of the following gives the number of boys that were at
or below Jaden’s height?
(A) 82
(B) 28
(C) 45
(D) 205
4. Landon took a competitive spelling test with 600 other area
students. When the results were announced, Landon found out
he scored in the 93rd percentile. Which of the following gives
the number of students who did better on the spelling test than
Landon?
(A) 7
(B) 65
(C) 93
(D) 42
5. The following box-and-whiskers
diagram gives the results on a recent
SAT math test.
(a) What is the 25th percentile score?
(b) What is the 50th percentile score?
(c) What is the 75th percentile score?
(d) What is the 100th percentile score?