12th Business Maths Monthly Test - 3 ( Probability Distributions )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Monthly Test - 3 ( Probability Distributions )-Aug 2020

Time : 2.30 Hours

Part - A

Generic 2 - Answer All Question

Defects in yarn manufactured by a local mill can be approximated by a distribution with a mean of 1.2 defects for every 6 metres of length. If lengths of 6 metres are to be inspected, find the probability of less than 2 defects.

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 .

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.

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
(il) less than 1,950 hours
(iii) more 1,920 hours but less than 2,100 hours.

Define Standard normal variate.

The mean of a binomial distribution is 5 and standard deviation is 2. Determine the distribution.

In a family of 3 children, what is the probability that there will be exactly 2 girls?

Define Poisson distribution.

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?

Assume that a drug causes a serious side effect at a rate of three patients per one hundred. What is the probability that atleast one person will have side effects in a random sample of ten patients taking the drug?

Part - B

Generic 5 - Answer All Question

Four coins are tossed simultaneously. What is the probability of getting
a) atleast 2 heads b) atmost 2 heads.

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.

In a book of 520 pages, 390 typo-graphical errors occur. Assuming Poisson law for the number of errors per page, find the probability that a random sample of 5 pages will contain no error.

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)

When counting red blood cells, a square grid is used, over which a drop of blood is evenly distributed. Under the microscope an average of 8 erythrocytes are observed per single square. What is the probability that exactly 5 erythrocytes are found in one square?

If the height of 300 students are normally distributed with mean 64.5 inches and standard deviation 3.3 inches find the height below which 99% of the student lie?

In a Poisson distribution the first probability term is 0.2725. Find the next Probability term

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)

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12th Business Maths Monthly Test - 3 ( Probability Distributions )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Monthly Test - 3 ( Probability Distributions )-Aug 2020

Part - A

Generic 2 - Answer All Question

Defects in yarn manufactured by a local mill can be approximated by a distribution with a mean of 1.2 defects for every 6 metres of length. If lengths of 6 metres are to be inspected, find the probability of less than 2 defects.

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 .

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.

Define Standard normal variate.

The mean of a binomial distribution is 5 and standard deviation is 2. Determine the distribution.

In a family of 3 children, what is the probability that there will be exactly 2 girls?

Define Poisson distribution.

Assume that a drug causes a serious side effect at a rate of three patients per one hundred. What is the probability that atleast one person will have side effects in a random sample of ten patients taking the drug?

Part - B

Generic 5 - Answer All Question

Four coins are tossed simultaneously. What is the probability of getting a) atleast 2 heads b) atmost 2 heads.

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.

In a book of 520 pages, 390 typo-graphical errors occur. Assuming Poisson law for the number of errors per page, find the probability that a random sample of 5 pages will contain no error.

When counting red blood cells, a square grid is used, over which a drop of blood is evenly distributed. Under the microscope an average of 8 erythrocytes are observed per single square. What is the probability that exactly 5 erythrocytes are found in one square?

If the height of 300 students are normally distributed with mean 64.5 inches and standard deviation 3.3 inches find the height below which 99% of the student lie?

In a Poisson distribution the first probability term is 0.2725. Find the next Probability term ​​​​​

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Tamilnadu Stateboardszs - Class

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 .

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.

Four coins are tossed simultaneously. What is the probability of getting
a) atleast 2 heads b) atmost 2 heads.

In a Poisson distribution the first probability term is 0.2725. Find the next Probability term