The document discusses the standard normal distribution, focusing on calculating areas under the standard normal curve and finding z-scores for given values. It includes multiple examples related to probabilities of events concerning osteoporosis onset and jellybean counts, as well as the heights of eighth-graders. Various exercises are presented to practice these concepts.

1. NORMAL DISTRIBUTION

2. STANDARD
NORMAL CURVE
The table for the
standard normal curve
reports the area under
the curve to the left (z <
z0) of various values for
the horizontal axis.

3. EXAMPLE 1:
What is the area under the curve to the
left of the z-score of −1.25?

4. CONVERTING TO A
Z-SCORE

5. EXAMPLE 2:
In a study of bone brittleness, the ages of people at the
onset of osteoporosis followed a normal distribution with a
mean age of 71 and a standard
deviation of 2.8 years.What z-score would an age of 65
represent in this study?

7. FINDING PROBABILITIES OF
EVENTS USING
Z-SCORES

8. EXAMPLE 3:
Using the same bone study as in example 2, find the probability of a random person
getting osteoporosis…
a) at the age of exactly 69
b) at an age under 69
c) at the age of at least 69
d) at an age between 69 and 72
e) at an age over 107

9. EXAMPLE 3:
Using the same bone study as in example 2, find the probability of a
random person getting osteoporosis…
a) at the age of exactly 69

10. EXAMPLE 3:
Using the same bone study as in example 2, find the probability of a
random person getting osteoporosis…
a) at the age of exactly 69

11. EXAMPLE 3:
Using the same bone study as in example 2, find the probability of
a random person getting osteoporosis…
b) at an age under 69

12. EXAMPLE 3: Using the same bone study as in example 2, find
the probability of a random person getting osteoporosis…
c) at the age of at least 69

13. EXAMPLE 3:
Using the same bone study as in example 2, find the probability of a
random person getting osteoporosis…
c) at the age of at least 69

14. EXAMPLE 3: Using the same bone study as in example 2, find
the probability of a random person getting osteoporosis…
d) at an age between 69 and 72

15. EXAMPLE 3: Using the same bone study as in example 2, find
the probability of a random person getting osteoporosis…
e) at an age over 107

16. Q1W3
NORMAL DISTRIBUTION
ACTIVITY 1

17. What is the area under the standard normal curve…
1) to the left
of z = 1.2
2) to the left
of z = 0.83
−
3) to the left
of z = 0
4) to the
right of z =
2.9
−
5) to the
right of z =
1.8
6) to the
right of z =
3.32
7) between
z = 0.37
−
and 0.37
8) between
z = 2.59
−
and 0.72
−

18. Q1W3
NORMAL DISTRIBUTION
ACTIVITY 2

19. a) Using = 113.7 and = 11.6
μ σ
convert…
1) an x value of 120.5 to a z-score
2) an x value of 99.9 to a z-score
3) an x value of 108.9 to a z-score
4) a z-score of 1.64 to an x value
−

20. B) for a study for stats class, the variable X represents the
number of jellybeans, modeled by a normal distribution.
Write a statement in the form P(X … ) for the probability
that…
1) there are more
than 2000
jellybeans
2) there are no
more than 2000
jellybeans
3) there are at
least 1775
jellybeans
4) there are
somewhere
between 1400 and
1500 jellybeans
5) there are at
most 2200
jellybeans
6) there are at
least 1850
jellybeans, but
fewer than 2150

21. C. In a certain school district, the distribution of the heights
of eighth-graders who play the tuba is approximately
normal, with a mean of 146.1 cm and a standard deviation of
8.4 cm. Determine the probability that a randomly chosen
tuba player from the eighth grade…
1) is shorter than 150 cm?
2) is at least 142 cm tall? 3) is 147.33 cm tall?
4) is taller than 158.3 cm? 5) is between 125 cm and 135 cm tall?
6) is between 145 cm and 147 cm tall?
7) is less than 110 cm tall?
8) is between 160 cm and 190 cm tall?

22. END OF SLIDES