12th Business Maths Weekly Test - 3 ( Probability Distributions )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 3 ( Probability Distributions )-Aug 2020

Time : 1.30 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

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

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

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

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

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

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

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

A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of number of success is

\(\frac83\)
\(\frac38\)
\(\frac45\)
\(\frac54\)

The variance of a binomial distribution is

equal to its mean
less than its mean
greater than its mean
none

Part - B

Generic 2 - Answer All Question

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.

Write down any five chief characteristics of Normal probability curve.

Mention the properties of poisson distribution.

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.

Part - C

Generic 3 - Answer All Question

The probability that a student get the degree is 0.4 Determine the probability that out of 5 students
(i) one will be graduate
(ii) atleast one will be graduate

The standard deviation of a binomial distribution (q+p)¹⁶ is 2. Find its mean.

A die is thrown 120 times and getting 1 or 5 is considered a success. Find the mean and variance of the number of successes.

Alpha particles are emitted by a radio active source at an average rate of 5 in a 20 minutes interval. Using Poisson distribution find the probability that there will be atleast 2 emission in a particular 20 minutes interval (e^-5 = 0.0067).

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

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12th Business Maths Weekly Test - 3 ( Probability Distributions )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 3 ( Probability Distributions )-Aug 2020

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:

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?

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?

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

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?

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?

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

A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of number of success is

The variance of a binomial distribution is

Part - B

Generic 2 - Answer All Question

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.

Write down any five chief characteristics of Normal probability curve.

Mention the properties of poisson distribution.

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.

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.

Part - C

Generic 3 - Answer All Question

The probability that a student get the degree is 0.4 Determine the probability that out of 5 students (i) one will be graduate (ii) atleast one will be graduate

The standard deviation of a binomial distribution (q+p)16 is 2. Find its mean.

A die is thrown 120 times and getting 1 or 5 is considered a success. Find the mean and variance of the number of successes.

Alpha particles are emitted by a radio active source at an average rate of 5 in a 20 minutes interval. Using Poisson distribution find the probability that there will be atleast 2 emission in a particular 20 minutes interval (e-5 = 0.0067).

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

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

The probability that a student get the degree is 0.4 Determine the probability that out of 5 students
(i) one will be graduate
(ii) atleast one will be graduate

The standard deviation of a binomial distribution (q+p)¹⁶ is 2. Find its mean.

Alpha particles are emitted by a radio active source at an average rate of 5 in a 20 minutes interval. Using Poisson distribution find the probability that there will be atleast 2 emission in a particular 20 minutes interval (e^-5 = 0.0067).