Module-7:
Estimation & Tests of Statistical Hypotheses :
Point Estimation, Confidence Intervals for Means, Confidence Intervals for
Difference of Two Means, Sample Size,
Tests About Proportions, Tests of the Equality of Two Normal Distributions, ChiSquare Goodness of Fit Tests, Contingency Tables, Tests of the Equality of
Several Means.
1.
If P(A) = 3/8, P(B) = ½ & P(A  B) = ¼ then find P(A/B), P(B/A), P( A / B ),
P( B / A )
2.
A man throws two disc. Find the probability of getting exactly 4 aces on
both in 6 trials.
3.
In a class 40 percent students read mathematics, 25 percent biology and
15 percent both mathematics & biology. One student is selected at
random find the probability that the reads mathematics, if it is known that
Biology the probability that he reads biology if the reads mathematics.
4.
If on an average 9 ships out of returns safe to a port, what is the
probability that out of 5 ships expected at least 3 will arrive?
(Ans:
12393/12500
5.
An event succeeds twice as many items as it falls. Find the probability that
in the next 6 trials it will succeed at least 4 times. (Ans: 496/729
6.
If the probability that a man and 60 will live to be 70 is 0.65, what is the
probability that out of 10 men, now 60, at least 7 will live to be 70? Ans:
0.510
7.
The number of telephone lines busy at an instant of time is electrical
variate with probability 6.2. If 10 lines are chosen at random.
What is the probability that 5 lines are busy? (Ans: 0.02642)
What is the probability that at most 2 lines are busy?
8.
The probability of a man hiting a target is l/4 (i) if he fires 7 times, What is
the probability of his hitting the target at least twice? (ii) IIow many times
must be fired so that the probability of the hitting the target atleast once is
greater then 2/3? (Ans: 0.5551,4).
9.
I percvent of defective items, What should be the number n of items in a
random sample, that the probability of finding at least one defective in it is
at least 0.95? (Ans: 68)
10.
The probability that a pen manufactured by a company will be defective is
0.1. If 12 such pens are selected at random, find the probability that (i)
exactly two will be defective (ii) atleast two will be defective (iii) none will
be defective. (Ans: 0.2301.0.3112.0.2823)
If on an average one ship in every ten is wreked, find the probability that
out of 5 ships expected to arrive, 4 at least will arrive safely.
11.
12.
10% of screws produced in a certain factory tum out to be defective find
the probability that in a sample of 10 screws chosen at random exactly two
will be defective.
13.
The probability that a man aged 60 will live to be 70 is 0.65 the probability
that out of 10 men, now 60, at least 7 will leave to be 70?
14.
An underground mine has 5 pumps installed for pumping out storm water,
the probability of any one of the pumps failing during the storm is 1/8, what
is the probability that at least 2 pumps will be working.
15.
If the probability of a defective bolt is 0.1 find (I) mean (II) the standerd
deviation for the distribution bolts in a total of 400.
16.
Die is tossed thrice. A success is getting 1 or 6 on a toss. Find the (i)
mean (ii) variance of the number of success.
17.
Assume that the probability of an individual coal miner being killed in a
mine accident during a year is 1/2400 use appropriate statistical
distribution to calculate the probability that in a mine employing 200
miners, there will be at least one fatal accident in a year
18.
In a certain factory producing cy cle tyres, there is a small chance of 1 in
500 tyres to be defective. The tyres are supplied in lots of 10. Using
poison distribution calculate the approximate number of lots containing no
defective, one defective and two defective tires, respectively, in a
consignment of 10,000 lots.
19.
Students of a class were given on aptitude test their marks were found to
be normally distributed with mean 60 and standard deviation 5. What
percentage of students scored more than 60 markets.
20.
It was found that 10 percent of boys in a certain class were suffering from
short sight. What is the probability that random sample of 5 boys will
certain (i) no boy suffering from short sight, (ii) exactly 1 boy suffering from
short sight (iii) not more than 4 boys suffering from shart sight.
(Ans: 0.2301, 0.3412.0.2823.
21.
Given that 2 percent of the fuses manufactured by a firm are detective.
Find the probability that a bvox containing 60 issues has (i) at least one
defective fuse (ii) 3 or more defective fuses.
(Ans: 0.982, 0.762)
22.
A car hire firm has 2 cars, which it hires day by day. The demand for car
on each day is distributed as a Poisson distribution with mean 1.5.
Calculate thej probability thatj on a certain day (i) neither car is used and
(ii) some demand is refused.
(Ans: 196)
23.
A manufacturer knows that 5 percent of items of his product is defective. If
he sell the items in boxes of 100 and guarantees that not more then 4
items will be defective, What is the probability that a box will fail to meet
the guaranteed quality. (Ans: 06620)
24.
Using Poisson’s distribution, find the probability that the ace of spaces will
be drawn from a pack of well-shuffled cards at least once in 104
consecutive trials. (Ans: 0.8647)
25.
In a sample survey of a large number of married couples it is found that
13.5 percent of them are without any children. If we as some what the
number of children per couple is a random variable with a Poisson
distribution find the percentage of couples having one child only.
(Ans:
27)
26.
Find the probability that at the most 5 defective fuses will be found in a
box of 200 fuses if experience shows that 2 percent of search fuses are
defective. (Ans: 0.785)
27.
Define Poison distribution and show that the Poisson distribution can be
regarded as the limiting form of the Binomial, Distribution Hence obtain the
mean and variance of Poisson distribution.
28.
Fit a Poisson’s distribution of the following data
Death
0
1
2
3
4
Freq.
122 60
15
2
1
29.
A hospital switch board receive: an average of four emergency calls in 16
minute interval. What is the probability that there at the most 2 emergency
call in a 10 minutes interval (ii) there are exacting 5 emergency calls is 10
minutes interval.