12th Business Maths Monthly Test - 2 ( Probability Distributions )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Monthly Test - 2 ( Probability Distributions )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

The starting annual salaries of newly qualified chartered accountants (CA's) in South Africa follow a normal distribution with a mean of Rs.1,80,000 and a standard deviation of Rs.10,000. What is the probability that a randomly selected newly qualified CA will earn between Rs.1,65,000 and Rs.1,75,000 per annum?

0.819
0.242
0.286
0.533

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

(2/3)⁶
(2/3)⁵(1/3)
(1/3)⁶
4(2/3)⁶

The time until 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?

0.0062
0.0668
0.8413
0.0228

For a binomial distribution

A B

1) skew symmetric (a) p = q = 0.5

2) positively skewed (b) p < 0.5

3) Variance is less than (c) p $\neq$ q

4) symmetrical (d) mean

The correct match is

1-c, 2-d, 3-b, 4 - a
1 - c, 2 - b, 3 - d, 4 - a
1 - a, 2-b, 3 - d, 4 - c
1 - d, 2 - c, 3- d, 4 - a

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

$\left( \frac { 2 }{ 3 } \right) ^{ 6 }$
$\left( \frac { 2 }{ 3 } \right) ^{ 5 }\left( \frac { 1 }{ 3 } \right) $
$\left( \frac { 1 }{ 3 } \right) ^{ 6 }$
$4\left( \frac { 2 }{ 3 } \right) ^{ 6 }$

The sum of the mean and variance of a binomial distribution for 6 trial is 2.16. Then p =_________

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:

1.00
-1.00
0.00
-0.41

In a Poisson distribution mean is 25, then S.D is

5
625
125
$\sqrt 5$

For a normal distribution if the mean is m, mode is n and median is m, then

m > m₁ > m₀
m < m₁ < m₀
m $\neq$ m₁ x m₀
m = m₁ = m₀

A B

1) Toss of a coin a) Binomial
distribution

2) Normal distribution b) Poisson
distribution

3) Number of suicides in a city c) Continuous distribution

4) Discrete distribution d) Bernoulli trial

The correct match is

1 - d, 2 - c, 3 - a, 4 - b
1 - d, 2 - c, 3 - b, 4 - a
1 - d, 2 - a, 3 - b, 4 - c
1 - d, 2 - b, 3 - c, 4 - a

If the variance of a Poisson distribution is 0.5. Then p(X = 3) is _________ (e^-05 = 0.6066).

0.1206
0.0126
0.1260
12.60

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

-0.48
0.48
-1.04
1.04

In a binomial distribution if the mean is 8 and the variance is 6, then the number of trials is

In 8 throws of a die, 1 or 3 is considered a success. Then the mean number of successes is

$\frac83$
$\frac43$
$\frac23$
$\frac53$

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:

1.00
-1.00
0.00
-0.41

Part - B

Generic 2 - Answer All Question

Mention the properties of binomial distribution.

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.

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.

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 $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

Write any 2 examples for Poisson distribution.

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?

Suppose X is a binomial variate X $\sim $ B (5, p) and P(X = 2) = P(X = 3), then find p.

Part - C

Generic 3 - Answer All Question

The mean of Binomials distribution is 20 and standard deviation is 4. Find the parameters of the distribution.

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

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.

The probability that an event A happens in one treat of an experiment is 0.4. Three independent treats of the experiment are performed. Find the probability that the event A happens at least once.
Assume the mean height of children to be 69.25 cm with a variance of 10.8 cm. How many children in a school of 1,200 would you expect to be over 74 cm tall?

The life of army shoes is normally distributed with mean 8 months and standard deviation 2 months. lf 5000 pairs are issued, how many pairs would be expected to need replacement within 12 months.

Verfy the following statement:
The mean of a Binomial distribution is 12 and its standard deviation is 4.

If x is a binomially distributed random variable with E(x) =2 and van (x)=4/3 Find P(x=5)

Part - D

Generic 5 - Answer All Question

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.

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

Marks in an aptitude test given to 800 students of a school was found to be normally distributed 10% of the students scored below 40 marks and 10% of the students scored above 90 marks. Find the number of students scored between 40 and 90?
The mean weight of 500 male students in a certain college is 151 pounds and the S.D is 15 pounds. Assuming the weights are normally distributed, find how many students weight
(i) between 120 and 155 pounds
(ii) more than 185 pounds.

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?

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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A	B
1) skew symmetric	(a) p = q = 0.5
2) positively skewed	(b) p < 0.5
3) Variance is less than	(c) p \(\neq\) q
4) symmetrical	(d) mean

A	B
1) Toss of a coin	a) Binomial distribution
2) Normal distribution	b) Poisson distribution
3) Number of suicides in a city	c) Continuous distribution
4) Discrete distribution	d) Bernoulli trial

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12th Business Maths Monthly Test - 2 ( Probability Distributions )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Monthly Test - 2 ( Probability Distributions )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

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

The time until 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?

For a binomial distribution A B 1) skew symmetric (a) p = q = 0.5 2) positively skewed (b) p < 0.5 3) Variance is less than (c) p \(\neq\) q 4) symmetrical (d) mean The correct match is

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

The sum of the mean and variance of a binomial distribution for 6 trial is 2.16. Then p =_________

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:

In a Poisson distribution mean is 25, then S.D is

For a normal distribution if the mean is m, mode is n and median is m, then

A B 1) Toss of a coin a) Binomial distribution 2) Normal distribution b) Poisson distribution 3) Number of suicides in a city c) Continuous distribution 4) Discrete distribution d) Bernoulli trial The correct match is

If the variance of a Poisson distribution is 0.5. Then p(X = 3) is _________ (e-05 = 0.6066).

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

In a binomial distribution if the mean is 8 and the variance is 6, then the number of trials is

In 8 throws of a die, 1 or 3 is considered a success. Then the mean number of successes is

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:

Part - B

Generic 2 - Answer All Question

Mention the properties of binomial distribution.

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.

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.

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?

Write any 2 examples for Poisson distribution.

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?

Suppose X is a binomial variate X \(\sim \) B (5, p) and P(X = 2) = P(X = 3), then find p.

Part - C

Generic 3 - Answer All Question

The mean of Binomials distribution is 20 and standard deviation is 4. Find the parameters of the distribution.

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

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.

The probability that an event A happens in one treat of an experiment is 0.4. Three independent treats of the experiment are performed. Find the probability that the event A happens at least once.

Assume the mean height of children to be 69.25 cm with a variance of 10.8 cm. How many children in a school of 1,200 would you expect to be over 74 cm tall?

The life of army shoes is normally distributed with mean 8 months and standard deviation 2 months. lf 5000 pairs are issued, how many pairs would be expected to need replacement within 12 months.

Verfy the following statement: The mean of a Binomial distribution is 12 and its standard deviation is 4.

If x is a binomially distributed random variable with E(x) =2 and van (x)=4/3 Find P(x=5)

Part - D

Generic 5 - Answer All Question

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.

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

Marks in an aptitude test given to 800 students of a school was found to be normally distributed 10% of the students scored below 40 marks and 10% of the students scored above 90 marks. Find the number of students scored between 40 and 90?

The mean weight of 500 male students in a certain college is 151 pounds and the S.D is 15 pounds. Assuming the weights are normally distributed, find how many students weight (i) between 120 and 155 pounds (ii) more than 185 pounds.

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?

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For a binomial distribution

A B

1) skew symmetric (a) p = q = 0.5

2) positively skewed (b) p < 0.5

3) Variance is less than (c) p \(\neq\) q

4) symmetrical (d) mean

The correct match is

A B

1) Toss of a coin a) Binomial
distribution

2) Normal distribution b) Poisson
distribution

3) Number of suicides in a city c) Continuous distribution

4) Discrete distribution d) Bernoulli trial

The correct match is

If the variance of a Poisson distribution is 0.5. Then p(X = 3) is _________ (e^-05 = 0.6066).

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.

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?

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 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.

Verfy the following statement:
The mean of a Binomial distribution is 12 and its standard deviation is 4.

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

The mean weight of 500 male students in a certain college is 151 pounds and the S.D is 15 pounds. Assuming the weights are normally distributed, find how many students weight
(i) between 120 and 155 pounds
(ii) more than 185 pounds.