M130:
Introduction to Probability and Statistics
Tutor Marked Assignment
Cut-Off Date: Dec 7th, 2013 Total Marks: 60
M130 TMA Feedback Form
Q−1: [2+3+3+1+1 Marks] Below are the earnings, for
a particular week, of 15 staff (including the owner) working in a small
business:
|
Weekly earnings (£)
|
280
|
370
|
305
|
285
|
480
|
1,260
|
210
|
340
|
280
|
290
|
315
|
325
|
370
|
360
|
280
|
a) Calculate the mean, median and mode.
b) Calculate the lower and upper quartiles, and find the
inter-quartile range.
c) Calculate the standard deviation of the earnings.
d) Find the range of the earnings.
e) Why might the range be an unhelpful measure of spread for
these particular data?
Q-2: [4+3+3Marks]
a) You are considering 10 different colleges. Before you decide
to apply to the colleges, you want to visit some or all of them. In how many
orders you can visit:
i-
6 of the colleges
ii-
All ten colleges
b) How many permutations are there of the letters in the word
BANANA?
c) A committee of 3 juniors and 3 seniors is to be formed from
the members of a club having 18 juniors and 15 seniors. How many different
committees are possible?
Q-3: [3+3+1+3Marks]
Suppose that city records produced the following probability data on a driver
being an accident on the last day of a Memorial Day Weekend.
|
|
Accident (A)
|
No accident (A’)
|
Total
|
|
Rain (R)
|
0.025
|
0.335
|
0.360
|
|
No rain (R’)
|
0.015
|
0.625
|
0.640
|
|
Total
|
0.040
|
0.960
|
1.00
|
a)
Find the probability of
accident rain or no rain.
b)
Find
the probability of rain, accident or no accident.
c)
Find
the probability of an accident and rain.
d)
Find
the probability of an accident, given rain.
Q-4: [2+2+3+3Marks]
A manufacturer has 3 machines
, make 20%, 30% and 50%,
respectively, of the products. It is known from past experience that 2%, 3% and
4% of the products made by each machine respectively are defective. If a
finished product is randomly selected:
, make 20%, 30% and 50%,
respectively, of the products. It is known from past experience that 2%, 3% and
4% of the products made by each machine respectively are defective. If a
finished product is randomly selected:
a) What is the probability that it is defective?
b) What is the probability that it is not defective?
c) If the product is defective, what is the probability it was
made by machine
?
?
d) If the product is
not defective, what is the probability that it was made by machine
?
?
Q-5: [2+2+3+2+3Marks]
A coin is tossed three times. Let X be a random variable representing the
number of heads in three tosses of a coin. The coin is unbalanced and a head
has a 60% chance of occurrence.
a) List the possible elements of the sample space S for the
three tosses of the coin and to each sample point assign a value x of X.
b) Find the probability distribution and the cumulative
distribution of the random variable X.
c) Find 
d) Find the mean of
the random variable X.
e) Calculate the
variance and standard deviation of the random variable X.
Q-6: [2+2+2+3+3Marks]
The density function for a random variable X is given by 
where k is a constant
where k is a constant
a) Find k.
b) Find 
c) Find p(x<1)
d) Find the mean and standard deviation.
e) Find the cumulative distribution function.
