Binomial distribution
1]An unbiased coin is tossed 3 times. Find the probability of 1] getting two head. 2] atleast two heads appear.
3] getting exactly two tails
2]An unbiased coin is tossed 5 times. Find the probability of getting
(i)three heads(ii)at least 4 heads (iii) getting 3 heads.
3]In 200 sets of tosses of 5 fair coins in how many ways you can expect
(i)at least two heads. (ii)at the most two heads.
4]An unbiased coin is tossed 6 times. Find the probability of getting atleast 4 heads.
5]Ten percent of screw product in a certain factory turn out to be defective. Find the probability in a sample of 10
screw at random, exactly two will be defective.
6]If 30% of the bulbs produced are defective, find the probability that out of 4 bulbs selected:
(i)One is defective (ii)At the most two are defective.
7]If 20% of the bolts produce by a machine are defective. Find the probability that out of 4 bolts drawn
i)One is defective ii)At most two are defective.
9]The probability that a pen manufactured by a company will be defective is 1/10. If 12 such pens are
manufactured, find the probability that :
(i)Exactly two will be defective. (ii)At least two will be defective. (iii)None will be defective
10]10% of the component manufactured by a company are defective. If 12 components are selected at random,
find the probability that atleast two will be defective.
11] From a box containing 100 screw, 20 of which are defective, 10 are selected at random. Find the probability
that, i)All will be defective ii)All are non-defective iii)At least one defective.
12] The probability that a man aged 65 will live to 75 is 0.65. What is the probability that out of 10 men which are
now 65, 7 will live to 75?
13] If the chance that out of 10 telephone lines. One of the line is busy at any instant is 0.2.
i)What is the chance that 5 of the lines are busy?
ii)What is the most probable number of busy line and what is the probability of this number?
14]The overall percentage of failures in a certain examination is 20. If six candidates appear in an examinations,
what is the probability that at least five pass the examination ?
Poisson distribution
1] If 5% of the electric bulbs manufacturing by a company are defective, use Poisson distribution to find the
probability that in a sample of 100 bulbs. (i)None is defective. (ii)Five bulbs are defective (Given e–5 = 0.007).
2] Using Poisson distribution, find the probability that the ace of spade will be drawn from a pack of well shuffled
cards at least once in 104 consecutive trials.
3] A firm produces articles of which 0.1 % are defective, out of 500 articles. If wholesaler purchases 100 such
cases, how many can be expected to have one defective? Given e-0 .5 = 0. 6065
4] If probability that an electric motor is defective is 0.01. What is probability that sample of 300 electric motor
will contain exactly 5 defective motor. (e–3 = 0.0498).
5] In sampling a large number of parts manufactured by a machine, the mean number of defectives in a sample of
20 is 2. Out of 1000 such samples, how many would be expected to contain atleast 3 defective parts.
6] If the probability of a bad reaction from a certain injection is 0.001, determine the chance that out of 2000
individuals more than two will get a bad reaction. (Given e2 = 7.4)
7] If 2% of the electric bulbs manufactured by a company are defective. Find the probability that in a sample of
100 Bulbs i)3 are defective ii)at least two are defective
8] If a random variable has a poisson distribution such that P(3) = P(4), find P(0) and P(1)
9] If P(2) = P(3), find P(5). (Given e3 = 20).
10] Fit a Poisson distribution for following observation
x
i
20 30 40 50 60 70
fi 8 12 30 10 6 4
A skilled typist, on routine work, kept a record of mistakes per day during 300 working days. Fit a Poisson
distribution to the set of observations.
x : 0 1 2 3 4 5 6
y : 143 90 42 12 9 3 1
normally distribution
1] I. Q.’s are normally distributed with mean 100 and standard deviation 15. Find the probability that a randomly
selected person has: (i)An I.Q. more than 130 (ii)An I.Q. between 85 and 115.
[ z = 2, Area = 0.4772, z = 1, Area = 0.3413]
2] In a sample of 1000 cases, the mean of certain test is 14 and standard deviation is 2.5. Assuming the
distribution to be normal. Find (i)How many students score between 12 and 15 ?
(ii)How many students score above 18 ? (Given : A(0.8) = 0.2881, A(0.4) = 0.1554, A((1.6) = 0.4452.)
3] In a certain examination 500 students appeared. Mean score is 68 with S.D. 8. Find the number of students
scoring. i)Less than 50 ii)More than 60.
(Given that area between z = 0 to z = 2.25 is 0.4878 and area between z = 0 to z = 1 is 0.3413).
4] In a test on 2000 electric bulbs, it was found that the life of particular make was normally distributed with
average life of 2040 hours and standard deviation of 60 hours. Estimate the no. of bulbs likely to burn for :
i)between 1920 hours and 2160 hours ii)more than 2150 hours
Given that : A(2) = 0.4772,A (1.83) = 0.4664.
5] In a certain examination 500 student appeared, mean score is 68 and S.D. 8. Assuming data are normally
distributed find the number of student scoring. a) Less than 50 b) More than 60.
(Given area between z = 0 to z = 2.25 is 0.4878 and area between z = 0 to z = 1 is 0.3413).
