Samacheer Kalvi solutions for Business Mathematics and Statistics [English] Class 12 TN Board chapter 7 - Probability Distributions [Latest edition]

Define Binomial distribution

Define Bernoulli trials

Derive the mean and variance of binomial distribution

Write down the condition for which the binomial distribution can be used.

Mention the properties 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 exactly three defectives

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 atleast two defectives

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 exactly 4 defectives

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 find the mean and variance

In a particular university 40% of the students are having newspaper reading habit. Nine university students are selected to find their views on reading habit. Find the probability that none of those selected have newspaper reading habit

In a particular university 40% of the students are having newspaper reading habit. Nine university students are selected to find their views on reading habit. Find the probability that all those selected have newspaper reading habit

In a particular university 40% of the students are having newspaper reading habit. Nine university students are selected to find their views on reading habit. Find the probability that atleast two-third have newspaper reading habit

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

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

If 18% of the bolts produced by a machine are defective, determine the probability that out of the 4 bolts chosen at random exactly one will be defective

If 18% of the bolts produced by a machine are defective, determine the probability that out of the 4 bolts chosen at random none will be defective

If 18% of the bolts produced by a machine are defective, determine the probability that out of the 4 bolts chosen at random atmost 2 will be defective

If the probability of success is 0.09, how many trials are needed to have a probability of atleast one success as 1/3 or more?

Among 28 professors of a certain department, 18 drive foreign cars and 10 drive local made cars. If 5 of these professors are selected at random, what is the probability that atleast 3 of them drive foreign cars?

Out of 750 families with 4 children each, how many families would be expected to have atleast one boy 

Out of 750 families with 4 children each, how many families would be expected to have atmost 2 girls

Out of 750 families with 4 children each, how many families would be expected to have 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, what is the probability that 3 will have a laptop?

Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that 12 of the travelers will not have a laptop?

Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that atleast three of the travelers have a laptop?

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes

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

Determine the binomial distribution for which the mean is 4 and variance 3. Also find P(X=15)

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?

Consider five mice from the same litter, all suffering from Vitamin A deficiency. They are fed a certain dose of carrots. The positive reaction means recovery from the disease. Assume that the probability of recovery is 0.73. What is the probability that atleast 3 of the 5 mice recover

An experiment succeeds twice as often as it fails, what is the probability that in next five trials there will be three successes

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

Define Poisson distribution

Write any 2 examples for Poisson distribution

Write the conditions for which the poisson distribution is a limiting case of binomial distribution

Derive the mean and variance of poisson distribution

Mention the properties of poisson distribution

The mortality rate for a certain disease is 7 in 1000. What is the probability for just 2 deaths on account of this disease in a group of 400? [Given e^–2.8 = 0.06]

It is given that 5% of the electric bulbs manufactured by a company are defective. Using poisson distribution find the probability that a sample of 120 bulbs will contain no defective bulb

A car hiring firm has two cars. The demand for cars on each day is distributed as a Poison variate, with mean 1.5. Calculate the proportion of days on which neither car is used

A car hiring firm has two cars. The demand for cars on each day is distributed as a Poison variate, with mean 1.5. Calculate the proportion of days on which some demand is refused

The average number of phone calls per minute into the switchboard 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 no phone at all

The average number of phone calls per minute into the switchboard 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 exactly 3 calls

The average number of phone calls per minute into the switchboard 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 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 no accident

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 atleast 2 accidents 

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 at most 3 accidents

Assuming that a fatal accident in a factory during the year is 1/1200, calculate the probability that in a factory employing 300 workers there will be at least two fatal accidents in a year, (given e^-0.25 = 0.7788).

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 no customer appears

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 three or more customers appear

Define Normal distribution

Define Standard normal variate

Write down the conditions in which the Normal distribution is a limiting case of binomial distribution

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 more than 2,150 hours

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 less than 1,950 hours

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 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 greater than 72 inches

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 less than or equal to 64 inches

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 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 a 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 ₹ 10,000 for each labour day spent in excess of 450. What is the probability that the company pay a penalty of at least ₹ 2,00,000?

Time taken by a construction company to construct a flyover is a normal variate with mean 400 labour days and a 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 ₹ 10,000 for each labour day spent in excess of 450. What is the probability that the company takes at most 500 days to complete the flyover?

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Normal distribution was invented by

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If X ~ N(9, 81) the standard normal variate Z will be

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If Z is a standard normal variate, the proportion of items lying between Z = – 0.5 and Z = – 3.0 is

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If X ~ N(µ, σ²), the maximum probability at the point of inflexion of normal distribution

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In a parametric distribution the mean is equal to variance is

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In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is

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The parameters of the normal distribution f(x) = `(1/sqrt(72pi))"e"^(-(x - 10)^2)/72 - oo < x < oo`

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A manufacturer produces switches and experiences that 2 percent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is :

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An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is

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If for a binomial distribution b(n, p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to

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The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are

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Forty percent of the passengers who fly on a certain route do not check in any luggage. The planes on this route seat 15 passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?

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Which of the following statements is/are true regarding the normal distribution curve?

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Which of the following cannot generate a Poisson distribution?

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The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84?

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The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of ₹ 180,000 and a standard deviation of ₹ 10,000. What is the probability that a randomly selected newly qualified CA will earn between ₹ 165,000 and ₹ 175,000?

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In a large statistics class, the heights of the students are normally distributed with a mean of 172 cm and a variance of 25 cm. What proportion of students is between 165cm and 181 cm in height?

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A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What proportion of calls lasts less than 180 seconds?

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Cape town is estimated to have 21% of homes whose owners subscribe to the satellite service, DSTV. If a random sample of your home is taken, what is the probability that all four homes subscribe to DSTV?

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Using the standard normal table, the sum of the probabilities to the right of z = 2.18 and to the left of z = – 1.75 is

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The time until the first failure of a brand of inkjet printers is normally distributed with a mean of 1,500 hours and a standard deviation of 200 hours. What proportion of printers fails before 1000 hours?

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The weights of newborn human babies are normally distributed with a mean of 3.2 kg and a standard deviation of 1.1 kg. What is the probability that a randomly selected newborn baby weight less than 2.0 kg?

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Monthly expenditure on their credit cards, by credit cardholders from a certain bank, follows a normal distribution with a mean of ₹ 1,295.00 and a standard deviation of ₹ 750.00. What proportion of credit cardholders spend more than ₹ 1,500.00 on their credit cards per month?

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Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be:

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If the area to the left of a value of z (z has a standard normal distribution) is 0.0793, what is the value of z?

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If P(Z > z) = 0.8508 what is the value of z (z has a standard normal distribution)?

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If P(Z > z) = 0.5832 what is the value of z (z has a standard normal distribution)?

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In a binomial distribution, the probability of success is twice as that of failure. Then out of 4 trials, the probability of no success is

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 no more than 2 rejects?

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 at least 2 rejects?

Hospital records show that of patients suffering from a certain disease 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover?

If electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week

Vehicles pass through a junction on a busy road at an average rate of 300 per hour. Find the probability that none passes in a given minute

Vehicles pass through a junction on a busy road at an average rate of 300 per hour. What is the expected number passing in two minutes?

Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Raghul wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Raghul takes the test and scores 585. Will he be admitted to this university?

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. Less than 19.5 hours?

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. Between 20 and 22 hours?

The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. What percent of people earn less than $40,000?

The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. What percent of people earn between $45,000 and $65,000?

The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. What percent of people earn more than $75,000

X is a normally distributed variable with mean µ = 30 and standard deviation σ = 4. Find P(X < 40)

X is a normally distributed variable with mean µ = 30 and standard deviation σ = 4. Find P(X > 21)

X is a normally distributed variable with mean µ = 30 and standard deviation σ = 4. Find P(30 < X < 35)

The birth weight of babies is Normally distributed with mean 3,500g and standard deviation 500g. What is the probability that a baby is born that weighs less than 3,100g?

People’s monthly electric bills in Chennai are normally distributed with a mean of ₹ 225 and a standard deviation of ₹ 55. Those people spend a lot of time online. In a group of 500 customers, how many would we expect to have a bill that is ₹ 100 or less?