Normal Distribution Assignment - Virtual High School (VHS) - MDM4U

PanHelp
MDM4U f1+, Mathematics for Data Management, University - Virtual High School (VHS)
Unit Assignment: Normal Distribution
Assignment Help | 100% Plagiarism Free | Success Assured | Email Now to get quote – admin@panhelp.com

1. Look at the sketches of continuous
probability distributions below.
A
B
C
For each sketch, give an example of a
situation which might give rise to such a
probability distribution, fully explaining
your reasoning.
A) A right-skewed distribution has a long right tail and are also called
positive-skew distributions. That is because, there is a long tail in the
positive direction on the number line; the mean is also to the right
of the beak. This probability distribution curve would occur if there
are more people below the median. To explain and apply my
reasoning to a situation; this could be the probability distribution
for the grades of a hard pop quiz in class. This could, as well,
represent the probability distribution of a person chosen at random
having a given income. This is because, income distribution
generally has a positive skew, so it’s probability distribution would
look like the diagram shown.
B) This is a constant hazard function (constant failure rate), so belongs
to the exponential distribution. This is also called a constant probability
distribution. This probability distribution curve would occur when all
events are of equal probability. For example, if rolling a fair 6-sided die,
the probability of getting any given side will create this probability
distribution curve. This is because for a constant probability
distribution, all possibilities are equally likely. This is one of the features
of rolling a fair die, every possibility comes up just as often as any other

1. Look at the sketches of continuous
probability distributions below.
A
B
C
For each sketch, give an example of a
situation which might give rise to such a
probability distribution, fully explaining
your reasoning.
C) This is a typical curve that shows a decreasing failure
probability rate. This sketch shows an extremely, large
probability at low values, like an asymptote. To explain, there
needs to be a situation where number leads to a smaller
probability. For instance, the offs are greatest for heads on a
penny coming up on the first attempt, than the longer strings
of tails before a heads comes up are increasingly unlikely. My
reasoning is that the most likely result is the smallest result,
and the odds of each higher result are smaller than the one
before it

2. In many situations, the normal
distribution can be used to approximate the
binomial distribution.
a. Explain the conditions in which this can
be done, and explain why we might want to
take advantage of this property.
b. Give an example of a situation in which
we could do this.
c. Give an example of a situation in which
we would not be able to make this
approximation and explain why.
a) For the normal distribution to be used to approximate the
situation, the number of trials and the probability must be
considered. It can be done if there are a sufficient number of trials
that would give more than 5 bars, which would give the required
shape. Also, the expected value must be at least 5 lower than the
number of trials. So to know if using a normal distribution would
be suitable, we need np ≥ 5, where n is the number of trials and p
is the probability, and n(1 − p) ≥ 5. This is useful because using a
normal distribution is, in many situations, much quicker and easier,
especially when there are a large number of trials.
b) We could do this when wanting to know the probability, for
instance, that a flight is delayed 20 times in the month of June,
when there is a 0.6 probability that it is delayed.
c) We could not use the normal distribution to approximate the
probability that a flight is delayed 3 times in one week, when there
is a 0.3 probability that it is delayed. This is because the expected
value of this would be less than 5, meaning that the curve of the
distribution would not be the same as the curve of a normal
distribution.

Please contact to get complete assignment
Email - admin@panhelp.com
3. A species of alien has a
mean height of 23 cm and a
standard deviation of 3.6 cm.
What is the probability that an
alien chosen at random has a
height of more than 20cm?

4. Researchers have observed
that regular smokers have an
average lifespan that is normally
distributed and is 68 years with
a standard deviation of 10 years.
What percent of smokers will
live beyond age 76?

5. The life span of a particular
species of turtle are normally
distributed with a mean of 180
years and a standard deviation of
40 years. What is the probability
that one of these turtles will live
more than a century?

6. A second species of alien
has a mean height of 71 cm and
a standard deviation of 5.3 cm.
An alientologist discovers that
30% of them bump their heads
getting into their spaceship.
What is the height of the
spaceship door?

7. In Bayfield, 65% of residents read
the Bayfield Breeze, a local online
blog. Dennis wants to know what
people think of the blog, so he
stops 40 people on the street to ask
them if they read it.
a. Verify that the normal distribution
can be used to approximate this
situation.
b. What is the mean and standard
deviation of the number of people he
finds that read the Breeze?
c. What is the probability that at least
25 of the people he asks read the
blog?

8. Yuen Zhi is running a ring toss
event at a school fair.
There is a 15% chance that
each attempt wins a prize. She
has 45 prizes and believes 250
people attempt the event.
She is worried she won't have
enough prizes. Can you reassure
her she will probably be ok?

9. We have been using the normal
distribution to approximate situations that
are in fact binomial events.
a. Demonstrate how accurate the
approximation is by using both approaches
to find the probability of the same event.
b. Describe the conditions under which
the normal would give a less accurate
approximation.
c. Explain a situation in which the criteria
for using the approximation would be met,
i.e. np ≥ 5 and n(1 - p) ≥ 5, and yet you
would decide not to use the normal
distribution.

Normal Distribution Assignment - Virtual High School (VHS) - MDM4U

More Related Content

Similar to Normal Distribution Assignment - Virtual High School (VHS) - MDM4U

More from Michael Taylor

Recently uploaded

Normal Distribution Assignment - Virtual High School (VHS) - MDM4U