If the average rain falls on 9 days in every thirty days, find the probability that rain will fall on atleast two days of a given week.

The sum and product of the mean and variance of a binomial distribution are 24 and 128. Find the distribution.

An insurance company has discovered that only about 0.1 per cent of the population is involved in a certain type of accident each year. If its 10,000 policy holders were randomly selected from the population, what is the probability that not more than 5 of its clients are involved in such an accident next year? (e⁻¹⁰=.000045)

One fifth percent of the the blades produced by a blade manufacturing factory turn out to be defective. The blades are supplied in packets of 10. Use Poisson distribution to calculate the approximate number of packets containing no defective, one defective and two defective blades respectively in a consignment of 1,00,000 packets (e^–0.2 =.9802)

If the probability that an individual suffers a bad reaction from injection of a given serum is 0.001, determines the probability that out of 2,000 individuals
(a) exactly 3, and
(b) more than 2 individuals will suffer a bad reaction.

What is the probability that a standard normal variate Z will be
(i) greater than 1.09
(ii) less than -1.65
(iii) lying between -1.00 and 1.96
(iv) lying between 1.25 and 2.75

If X is a normal variate with mean 30 and SD 5. Find the probabilities that 
(i) 26 ≤ X ≤ 40
(ii) X > 45

The average daily sale of 550 branch offices was Rs.150 thousand and standard deviation is Rs. 15 thousand. Assuming the distribution to be normal, indicate how many branches have sales between
(i) Rs. 1,25,000 and Rs. 1, 45, 000
(ii) Rs. 1,40,000 and Rs. 1,60,000

The marks obtained in a certain exam follow normal distribution with mean 45 and SD 10. If 1,300 students appeared at the examination, calculate the number of students scoring
(i) less than 35 marks and
(ii) more than 65 marks.

900 light bulbs with a mean life of 125 days are installed in a new factory. Their length of life is normally distributed with a standard deviation of 18 days. What is the expected number of bulbs expire in less than 95 days?

A bank manager has observed that the length of time the customers have to wait for being attended by the teller is normally distributed with mean time of 5 minutes and standard deviation of 0.6 minutes. Find the probability that a customer has to wait
(i) for less than 6 minutes
(ii) between 3.5 and 6.5 minutes

A sample of 125 dry battery cells tested to find the length of life produced the following resultd with mean 12 and SD 3 hours. Assuming that the data to be normal distributed , what percentage of battery cells are expected to have life
(i) more than 13 hours
(ii) less than 5 hours
(iii) between 9 and 14 hours

Derive the mean and variance of binomial distribution.

If 5% of the items produced turn out to be defective, then find out the probability that out of 20 items selected at random there are
(i) exactly three defectives
(ii) atleast two defectives
(iii) exactly 4 defectives
(iv) find the mean and variance

In a particular university 40% of the students are having news paper reading habit. Nine university students are selected to find their views on reading habit. Find the probability that
(i) none of those selected have news paper reading habit
(ii) all those selected have news paper reading habit
(iii) atleast two third have news paper reading habit.

If 18% of the bolts produced by a machine are defective, determine the probability that out of the 4 bolts chosen at random
(i) exactly one will be defective
(ii) none will be defective
(iii) atmost 2 will be defective

Out of 750 families with 4 children each, how many families would be expected to have
(i) atleast one boy
(ii) atmost 2 girls
(iii) and children of both sexes? Assume equal probabilities for boys and girls.

Forty percent of business travellers carry a laptop. In a sample of 15 business travelers,
(i) what is the probability that 3 will have a laptop?
(ii) what is the probability that 12 of the travelers will not have a laptop?
(iii) what is the probability that atleast three of the travelers have a laptop?

An experiment succeeds twice as often as it fails, what is the probability that in next five trials there will be
(i) three successes and
(ii) at least three successes

Derive the mean and variance of poisson distribution.

A car hiring firm has two cars. The demand for cars on each day is distributed as a Poisson variate, with mean 1.5. Calculate the proportion of days on which
(i) Neither car is used
(ii) Some demand is refused

The average number of phone calls per minute into the switch board of a company between 10.00 am and 2.30 pm is 2.5. Find the probability that during one particular minute there will be
(i) no phone at all
(ii) exactly 3 calls
(iii) atleast 5 calls

The distribution of the number of road accidents per day in a city is poisson with mean 4. Find the number of days out of 100 days when there will be
(i) no accident
(ii) atleast 2 accidents and
(iii) at most 3 accidents.

The average number of customers, who appear in a counter of a certain bank per minute is two. Find the probability that during a given minute
(i) No customer appears
(ii) three or more customers appear 

Write down any five chief characteristics of Normal probability curve.

In a test on 2,000 electric bulbs, it was found that bulbs of a particular make, was normally distributed with an average life of 2,040 hours and standard deviation of 60 hours. Estimate the number of bulbs likely to burn for
(i) more than 2,150 hours
(ii) less than 1,950 hours
(iii) more 1,920 hours but less than 2,100 hours.

In a distribution 30% of the items are under 50 and 10% are over 86. Find the mean and standard deviation of the distribution.

X is normally distributed with mean 12 and sd 4. Find P(X ≤ 20) and P(0 ≤ X ≤ 12)

If the heights of 500 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches , how many students have height
(a) greater than 72 inches
(b) less than or equal to 64 inches
(c) between 65 and 71 inches

In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take less than 16.35 seconds to develop prints.

Time taken by a construction company to construct a flyover is a normal variate with mean 400 labour days and standard deviation of 100 labour days. If the company promises to construct the flyover in 450 days or less and agree to pay a penalty of Rs. 10,000 for each labour day spent in excess of 450. What is the probability that
(i) the company pays a penalty of atleast Rs. 2,00,000?
(ii) the company takes at most 500 days to complete the flyover?

A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain
(a) no more than 2 rejects?
(b) at least 2 rejects?

Vehicles pass through a junction on a busy road at an average rate of 300 per hour.
1. Find the probability that none passes in a given minute.
2. What is the expected number passing in two minutes?

The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time .
a) less than 19.5 hours?
b) between 20 and 22 hours?

The annual salaries of employees in a large company are approximately normally distributed with a mean of Dallor. 50,000 and a standard deviation of Dallor.20,000.
(a) What percent of people earn less than Dallor.40,000?
(b) What percent of people earn between Dallor.45,000 and Dallor.65,000?
(c) What percent of people earn more than Dallor.70,00

X is a normally normally distributed variable with mean μ = 30 and standard deviation σ = 4. Find
(a) P(x < 40)
(b) P(x > 21)
(c) P(30 < x < 35)