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

St. Britto Hr. Sec. School - Madurai

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

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

If Z is a standard normal variate, then p(0 < Z < \(\infty\)) is

0.5
1
0.25
0.75

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

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

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

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

0
0.5
1
0.75

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

0.138
0.428
0.766
0.262

The probability that a normal variate X lies in the interval (\(\mu - \sigma, \mu + \sigma\)) is

0.0027
0.9973
0.6826
0.9544

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

-0.48
0.48
1.04
-0.21

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

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

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

\(\frac { 240 }{ 729 } \)
\(\frac { 489 }{ 729 } \)
\(\frac { 496 }{ 729 } \)
\(\frac { 251 }{ 729 } \)

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

0.819
0.242
0.286
0.533

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

5
625
125
\(\sqrt 5\)

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

4
128
256
20

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

Part - B

Generic 5 - Answer All Question

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

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?

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.

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)

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)

Assuming one in 80 births is a case of twins, calculate the probability of 2 or more sets of twins on a day when 30 births occur.
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.

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