Assignment II Questions

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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