Download Normal Distribution

Fri
5/27
Learning Objective:
To analyze normal
distribution
Lesson Hw: 11 – 10 WS 1
11 – 10
Algebra II
 To
find normal distribution
Discrete Probability Distribution – has
a finite number of possible events, or
values
Continuous Probability Distribution –
Events can be any value in an interval of
real numbers. Large data set
Normal Distribution – data that vary
randomly from the mean. Normal Curve
Skewed Data – distribution is an
asymmetric curve where one end
stretches out further than the other
end
- Data do not vary predictably from the
mean
- Do not use mean & standard deviation
to estimate percentages for skewed data
1. Sketch a normal curve for each of
the distribution. Label the x – axis
values at one, two, and three standard
deviation from the mean.
Mean = 15.7
Std Deviation = 2.8
34% 34%
13.5% 2.35%
2.35% 13.5%
7.3 10.1 12.9 15.7 18.5 21.3 24.1
2. Sketch a normal curve for each of
the distribution. Label the x – axis
values at one, two, and three standard
deviation from the mean.
Mean = 21.1
Std Deviation = 4.7
4.7
4.7
4.7
34% 34%
4.7
13.5% 2.35%
2.35% 13.5%
7
11.7 16.4 21.1 25.8 30.5 35.2
3. The bar graph gives the weights of a
population of female brown bears. The curve
shows how the weights are normally
distributed about the mean, 115 kg.
Approximately what percent of the female
brown bears weight between 100 and 129 kg.
23% + 42% + 23%
= 88%
4. Approximately what percent of the female
brown bears weight less than 120 kg.
23% + 42% + 5%
= 70%
less than 120 kg
5. The standard deviation in the weights of
female brown bears is about 10 kg.
Approximately what % of the female brown
bears have weights that are within 1.5
standard deviation of the mean? = 88%
mean
23% + 42% + 23%
6. The height of adult males are
approximately normally distributed with
mean 69.5 and standard deviation 2.5.
What % of adult males are between 67 in.
and 74.5 in. tall
σ =2.5
34% 34%
2.35% 13.5%
62 64.5 67
69.5
13.5% 2.35%
72
74.5 77
34% + 34% + 13.5% = 81.5%
7. In a group of 2000 adult males, about
how many would you expect to be taller
than 6 ft? (or 72 in.)
34% 34%
2.35% 13.5%
62 64.5 67
69.5
13.5% 2.35%
72
74.5 77
2.35% + 13.5% = 15.85%
(2000)(0.1585)
= 317
8. The scores on the Algebra 2 final are
approximately normally distributed with a
mean of 150 and a standard deviation of
15. What % of the students who took the
tests scored about 180?
σ =15
34% 34%
2.35% 13.5%
105 120 135
150
13.5% 2.35%
165 180 195
= 2.35%
9. The scores on the Algebra 2 final are
approximately normally distributed with a mean
of 150 and a standard deviation of 15. If 250
students took the final, approximately how
many scored above 135?
34% 34%
13.5% 2.35%
2.35% 13.5%
105 120 135 150 165 180 195
(34%+34%+13.5%+2.35%)
(250)(0.8385) = 209