NATIONAL INSTITUTE OF TECHNOLOGY WARANGAL
WARANGAL – XXXXXXXXXX
DEPARTMENT OF MATHEMATICS
1. A family has eight children. What is the probability that there being seven boys and one girl,
assuming that a boy is as likely to be born as a girl? What is the probability of there being
etween three to five boys? How many children should be born to be 95% sure of having a girl?
Ans: 0.71, 5
2. On average, one widget in 100 manufactured at a certain plant is defective. Assuming that
defects occur independently, what is the distribution of defective parts in a batch of 48? Use the
Poisson approximation to the binomial to compute the probability that there is more than one
defective part in a batch of 48? Ans: 0.38
3. The weight of items (in kilograms) are assumed to follow the normal distribution. From a market
the following data are recorded: 10:03% of the items are under 25 kilogram weight and 89:97%
of the items are under 70 kilograms weight. What are the mean and standard deviation of the
distribution. Ans: 17.58, 47.5
4. In an engineering college, it is observed that there are 500 students taking a Mathematics
course. The probability of the need for a particular book from college li
ary for any students is
0.07. How many copies of that book should be kept in the li
ary so that the probability may be
greater than 0.95 that none of the students needing a copy from the li
ary has to go back
disappointed? (Assume normal distribution.) Ans: 45
5. An insurance company found that only 0.01%of the population is involved in a certain type of
accident each year. If its 1000policy holders were randomly selected from the population, what
is the probability that not more than two clients are involved in such an accident next year?
Ans: 0.9998
6. A fair dice is thrown 600 times. Find the lower bound for the probability of getting 80 to 120
sixes. Ans:0.792
7. For a random variable ? with pdf ?(?) =
?−???
?!
, ? > 0, ? ≥ 0 is an integer, show that
?[0 < ? < 2? + 4]
?
? + 1
.
8. Let ? denote the number of accidents in a factory per week having pmf ?(?) =
?
(?+1)(?+2)
, ? =
0,1,2,… Find the value of ?, ?[?] and the median of ? .
9. A person with ? keys want to open the door and tries the keys independently at random. Find
the expectation of the number of trials required to open the door. (Assume that unsuccessful
keys are eliminated). Ans: (? + 1)/2
10. Show that the median and mode of a normal distribution are the same as the mean.