22CEBS401 –
PROBABILITY AND STATISTICS FOR CIVIL ENGINEERING
ASSIGNMENT- II
PART A
1.
Define Arithmetic mean of a grouped data.
2.
What are the four scales of data
classification?
3.
What do you mean by histogram?
4.
Define percentile.
5.
What do you mean by Bernoulli distribution?
6.
Define Poisson distribution.
7.
What is a "random variable”?
8.
What is the use of Chi-square distribution?
PART B
1.
Two unbiased dice are thrown. Find the
probability that both the dice show the same number.
2.
What are independent events? Illustrate with
an example.
3.
A construction crew is investigating the
daily wind speed (km/h) at a potential bridge construction site. The following
data is collected for a two-week period:
10, 15, 12, 18, 20, 16, 14, 11, 13, 17,
22, 19, 21, 25.
Construct a frequency table or histogram
to represent the wind speed data.
4.
What do you mean by conditional probability?
In what way can a Civil Engineer use it?
5.
A fair coin is tossed 6 times. Find the
probability of getting exactly 4 heads using Binomial distribution.
6.
A car hire firm has two cars which it hires
out day by day. The no. of demands for a car on each day is distributed as
Poisson distribution with mean 1.5. Calculate the proportion of days on which
there is no demand.
7.
A non-destructive testing method is used to
evaluate concrete cores drilled from a building foundation. The test result can
either be a "pass" or "fail." If the probability of a
single core passing the test is 0.8, what is the probability of encountering
exactly 2 failures in a random sample of 5 cores tested? (Binomial
Distribution)
8.
A city gets rain on average 2 days a week.
What is the chance of exactly 3 rainy days in a week? (Use Poisson
distribution)
PART C
1. An
urn contains 10 white and 3 black balls. Another urn contains 3 white and 5
black balls. Two balls are drawn at random from the first urn and placed in the
second urn and then 1 ball is taken at random from the latter. What is the
probability that it is a white ball?
2.
a.
State Bayes Theorem.
b.
A bag contains 5 balls and it is not known
how many of them are white. 2 balls are drawn at random from the bags and they
are noted to be white. What is the chance all the balls in the bag are white?
3.
a.
State Bernoulli’s theorem.
b.
If 10% of screws produced by automatic
machine are defective,
find
the probability that out of 20 screws selected at random, there are
i)
exactly 2 defective
ii)
utmost 3 defective
iii)
atleast 2 defectives
iv)
between 1 and 3 defectives (inclusive)
4.
List
the Properties of Poisson Distribution.
The
average number of phone calls per minute coming into a switch board between 2
PM and 4 PM is 2.5. Determine the probability that during one particular
minute, there will be
i)
4 or fewer
ii)
more than 6 calls.
5.
a.
Find the median from the following: 57,58,
61,42,38,65,72,66
b.
The score of two cricketers A & B are
given, find who is the better runner and consistent?
A B
40 28
25 70
19 31
80 0
38 14
8 111
67 66
121 31
66 25
76 4
6.
a.
Find the variance for the discrete data given
below:
i) 4,5,2,8,7 ii) 6,7,10,1213,4,8,12
b.
Calculate the standard deviation of the
following test data. Test Scores:
[22, 99, 102, 33, 57]
7.
a.
If a coin is tossed 5 times, using Binomial
distribution find the probability of:
i) Exactly 2 heads ii) Atleast 4 heads.
b.
In a cafe, the customer arrives at a mean
rate of 2 per minute. Find the probability of arrival of 5 customers in 1
minute using the Poisson distribution formula.
8.
Differentiate between the Binomial and
Poisson distribution with examples.
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