12th Business Maths Weekly Test - 1 ( Probability Distributions)

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 1 ( Probability Distributions)-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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 :

0.5443
0.4543
0.5543
0.4573

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

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

5
625
125
\(\sqrt 5\)

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

0.4987
0.1915
0.3072
0.3098

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:

0.4854
0.4599
0.0146
0.0547

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

0.0613
0.613
0.00613
0.3913

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

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

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

(a) it is symmetrical and bell shaped curve
(b) it is asymptotic in that each end approaches the horizontal axis but never reaches it
(c) its mean, median and mode are located at the same point
(d) all of the above statements are true.

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 are between 165 cm and 181cm in height?

0.954
0.601
0.718
0.8833

Part - B

Generic 2 - Answer All Question

Mention the properties of poisson distribution.

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

A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or under size. What is the probability that a batch of 10 pistons will contain

(a) no more than 2 rejects? (b) at least 2 rejects?

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

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?

Part - C

Generic 3 - Answer All Question

A fair coin is tossed 6 times. Find the probability that exactly 2 heads occurs.

Find the value of K if X is a normal variate whose p.d.f is given by f(x) = \(\frac1K\)\({e }^{ { 8x-4x }^{ 2 } }\), -\(\infty\) < X < \(\infty\)
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.

A and B play a game in which their chance of winning are in the ratio 3:2 Find A’s chance of winning atleast three games out of five games played.

If on an average 1 ship out of 10 do not arrive safely to ports. Find the mean and the standard deviation of ships returning safely out of a total of 500 ships.

If the chance of running a bus service according to schedule is 0.8, calculate the probability on a day schedule with 10 services :
(i) exactly one is late
(ii) atleast one is late

Part - D

Generic 5 - Answer All Question

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?
20% of the bolts produced in a factory are found to be defective. Find the probability that in a sample of 10 bolts chosen at random exactly 2 will be defective using
(i) Binomial distribution
(ii) Poisson distribution (e^-2 = 0.1353)

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?

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)

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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

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12th Business Maths Weekly Test - 1 ( Probability Distributions)

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 1 ( Probability Distributions)-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

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 :

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

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

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

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:

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

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

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

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

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 are between 165 cm and 181cm in height?

Part - B

Generic 2 - Answer All Question

Mention the properties of poisson distribution.

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

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?

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

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

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?

Part - C

Generic 3 - Answer All Question

A fair coin is tossed 6 times. Find the probability that exactly 2 heads occurs.

Find the value of K if X is a normal variate whose p.d.f is given by f(x) = \(\frac1K\)\({e }^{ { 8x-4x }^{ 2 } }\), -\(\infty\) < X < \(\infty\)

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.

A and B play a game in which their chance of winning are in the ratio 3:2 Find A’s chance of winning atleast three games out of five games played.

If on an average 1 ship out of 10 do not arrive safely to ports. Find the mean and the standard deviation of ships returning safely out of a total of 500 ships.

If the chance of running a bus service according to schedule is 0.8, calculate the probability on a day schedule with 10 services : (i) exactly one is late (ii) atleast one is late

Part - D

Generic 5 - Answer All Question

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?

20% of the bolts produced in a factory are found to be defective. Find the probability that in a sample of 10 bolts chosen at random exactly 2 will be defective using (i) Binomial distribution (ii) Poisson distribution (e-2 = 0.1353)

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?

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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 manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or under size. What is the probability that a batch of 10 pistons will contain

(a) no more than 2 rejects? (b) at least 2 rejects?

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.

If the chance of running a bus service according to schedule is 0.8, calculate the probability on a day schedule with 10 services :
(i) exactly one is late
(ii) atleast one is late

20% of the bolts produced in a factory are found to be defective. Find the probability that in a sample of 10 bolts chosen at random exactly 2 will be defective using
(i) Binomial distribution
(ii) Poisson distribution (e^-2 = 0.1353)