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12th Business Maths Weekly Test - 4 ( Probability Distributions )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 4 ( Probability Distributions )-Aug 2020

Time : 1.00 Hours

Part - A

Multiple Choice Question - Answer All Question

The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, the probability that he hits the target is

1
1 - (0.7)¹⁰
(0.7)¹⁰
(0.3)¹⁰

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

2.5 e^-1
e^-1
2 e^-1
none of the above

In a binomial distribution if n = 5, p(x = 3) = 2. p(x = 2), then p = _________

2q
2p
q
\(\frac { 2q }{ .3 } \)

In a poison distribution, mean is 16, then standard deviation is

4
128
256
20

Normal distribution was invented by

Laplace
De-Moivre
Gauss
all the above

A die is thrown 10 times. Getting a number greater than 3 is considered a success. The S.D of the number of successes is

2.5
1.58
5
25

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?

-1.41
1.41
-2.25
2.25

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

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

The area under the standard normal curve between z = -\(\infty\) and z = \(\infty\) is

0
0.5
1
0.75

For the standar-d normal distribution

A B

1) Area under the curve (a) 99.74%

2) Area between z = - 1 and z = 1 (b) 95.44%

3) Area between z = - 2 and z = 2 (c) 68.26%

4) Area between z = - 3 and z = 3 (d) 1

The correct match is

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

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

For a Poisson distribution

A B

1) Never (a) \(\frac { { e }^{ -\lambda }.\lambda ^{ 0 } }{ x! } \), x=0,1,2,3

2) p(x) (b) symmetrical

3) mean (c) small

4) n is large and p is (d) \(\lambda\)

The correct match 1s

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

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

The parameters of the normal distribution f(x) = \(\left( \frac { 1 }{ \sqrt { 72\pi } } \right) \frac { { e }^{ -(x-10)^{ 2 } } }{ 72 } \)-\(\infty\)<x<\(\infty\)

(10,6)
(10,36)
(6,10)
(36,10)

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

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

0.487
0.392
0.500
0.791

For a binomial distribution with mean 2 and variance \(\frac43\), p=_________

\(\frac23\)
\(\frac13\)
\(\frac34\)
\(\frac { 2 }{ \sqrt { 3 } } \)

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?

6.00
6.45
7.20
7.50

The parameters of the normal distribution \(f(x)=\left( \frac { 1 }{ \sqrt { 72\pi } } \right) \frac { { e }^{ -(x-10)^{ 2 } } }{ 72 } -\infty <X<\infty \)

(10,6)
(10,36)
(6,10)
(36,10)

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

2.5 e^-1
e^-1
2e^-1
none of the above

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

\(Z=\frac { X-81 }{ 9 } \)
\(Z=\frac { X-9 }{ 81 } \)
\(Z=\frac { X-9 }{ 9 } \)
\(Z=\frac { 9-X }{ 9 } \)

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 172cm and a variance of 25cm. What proportion of students are between 165cm and 181cm in height?

0.954
0.601
0.718
0.883

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

Normal distribution was invented by

Laplace
De-Moivre
Gauss
all the above

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

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

If the mean of the binomial distribution is 25, then its standard deviation lies in the interval

[0, 5)
(0, 5]
[0, 25]
(0,25]

For a standard normal distribution, the mean and variance are _________

\(\mu, \sigma^2\)
\(\mu, \sigma\)
0, 1
1, 1

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

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