Download 12. Maths Assign - graded version B

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12. Maths Assign – graded version B
Access to HE Diploma in Science
Higher Skills in Mathematics – Normal Distribution and
Testing RB1/3/AA/05G
Normal Distribution
Assignment briefing and mapping to unit:
Timed examination
Time: 1.5 hours
You should attempt ALL questions.
The use of a scientific calculator is allowed. The use of any pre-programming facility
is not allowed.
Give non-exact numerical answers correct to an appropriate degree of accuracy,
unless otherwise stated.
You are permitted to take into the examination 1 sheet of A4 paper with notes and/or
examples of your choice. Normal distribution tables will be provided.
IN ORDER TO ACHIEVE PASS:
You must achieve all the required grading criteria successfully, complete all
questions in Section A and achieve at least 90 %
IN ORDER TO ACHIEVE A MERIT in Application of Skills – Section B:
You must achieve all the requirements for a PASS and achieve at least 40%
IN ORDER TO ACHIEVE A DISTINCTION in Application of Skills – Section B:
You must achieve all the requirements for a MERIT and achieve at least 80%
Assignment hand out date:
Assignment submission deadline date:
Draft(s) permitted: Yes/No
If yes, include deadline date(s) for draft(s)
Mapping to Unit
This assignment covers the following learning outcomes & assessment criteria.
1.Understand normal distribution
1.1.Obtain percentages of a skewed distribution using standard deviations
1.2.Explain what is meant by a skewed distribution
1.3.Calculate the z score
1.4.Use published tables for the normal distribution to calculate probabilities
Section A
1) Find the percentage area under the standard normal curve:
a) between 1 and 2 standard deviations from the mean
b) between 0.5 and 1.5 standard deviations from the mean
(4 marks)
2) Find the percentage area under the standard normal curve which is more
than:
a) 1 standard deviation above the mean
b) 2.4 standard deviations above the mean.
(4 marks)
3) Find the percentage area under the standard normal curve that is less than:
a) 1 standard deviation below the mean
b) 1.75 standard deviations below the mean.
(4 marks)
4) The random variable X~N(12,22). Find by calculating the Z score
a) P (X < 15)
b) P (X > 10)
c) P (9 < X < 13)
d) P (11.5 < X < 14.3)
(12 marks)
5) A biologist has studied a particular tropical insect and she has discovered
that its lifespan is normally distributed. The mean lifespan of this insect is 72
days, and the standard deviation of its lifespan is eight days. Find the
probability that the next insect studied lives:
a) fewer than 70 days
b) more than 76 days
c) between 68 and 78 days.
(9 marks)
6) Explain with the aid of diagrams and by reference to mode, mean and
median what you understand by the terms:
a) positively skewed
b) negatively skewed.
(8 marks)
Section B
7) The heights of female students at a large university are normally distributed
with a mean of 168 cm and a standard deviation of 8 cm. One of these
students is chosen at random. Find the probability that her height is:
a) greater than 172 cm
b) between 160 cm and 170 cm
c) Given that 70% of all these female students have heights greater than
H cm, find the value of H, correct to one decimal place.
(20 marks)
The heights of male students at the university are normally distributed with a
mean of 178cm and 60% of all males being between 170cm and 186cm.
d) Find the standard deviation of the height of the male students.
e) Find the probability that a male student will be greater than 182cm in
height.
(20 marks)
Grading information for this assignment
Grade descriptor:
For a pass you
should:
For a merit you
should:
For a distinction
you should:
Additional
Guidance notes
7: Quality
Meet the assessment criteria to achieve the learning outcomes for the
unit
The student’s work, taken as a whole, demonstrates a very good
response to the demands of the assignment.
The student’s work, taken as a whole, demonstrates an excellent
response to the demands of the assignment.
Remember to show all of your workings
Grade descriptor:
For a pass you
should:
For a merit you
should:
3: Application of Skills
Meet the assessment criteria to achieve the learning outcomes for the
unit
The student’s work or performance generally selects appropriate
techniques and applies appropriate methods with very good levels of
accuracy. Note: See also criteria under Assignment briefing and
mapping to unit section.
The student’s work or performance generally selects appropriate
techniques and applies appropriate methods with excellent levels of
accuracy. Note: See also criteria under Assignment briefing and
mapping to unit section.
Remember to show all of your workings
For a distinction
you should:
Additional
Guidance notes
Declaration: I confirm that this assignment is all my own work and that it conforms to the
course policy on plagiarism as stated in the course handbook.
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