Sipnayan Quiz 2021

Welcome, faculties and participants!

Mechanics:

1. The coverage of the Sipnayan Quiz are the topics from General mathematics and Statistics and Probability.

2. There will be three (3) components in the competition namely: Easy (10 questions), Average (10 questions) and Difficult round (5 questions).

3. The host will read the question twice, the students may start answering once the time-limit starts. (20 seconds - easy, 30 seconds - average, 1 minute - difficult)

4. The participants are allowed to use calculators and table of probability distributions (binomial, poisson, normal distribution.)

5. The top three scorers will automatically declared as the 3rd placer, 2nd placer and champion of Sipnayan Quiz 2021.

EASY ROUND

20 seconds

1. An ordered pair is represented by _______.

(Input, Output)

(Input, Input)

(Output, Input)

(Output, Output)

Multiple Choice

1. An ordered pair is represented by _______.

• (Input, Output)

• (Input, Input)

• (Output, Input)

• (Output, Output)

2. Which of the following is an example of continuous random variable?

Number of children in a family

Number of “heads” flipped in three trials

height of girls in a class

number of patients a doctor sees in a day

Multiple Choice

2. Which of the following is an example of continuous random variable?

• Number of children in a family

• Number of “heads” flipped in three trials

• height of girls in a class

• number of patients a doctor sees in a day

3. Simplify: -4²

Fill in the Blank

3. Simplify: -4²

4. The possible values of a certain random variable are 0, 1, 2, and 3 with the probabilities of 0.1, 0.2, 0.3, and 0.4 respectively. What is the mean of such random variable?

Fill in the Blank

4. The possible values of a certain random variable are 0, 1, 2, and 3 with the probabilities of 0.1, 0.2, 0.3, and 0.4 respectively. What is the mean of such random variable?

5. Which of these is a one to one function?

f={(1,2),(3,4)(5,6),(8,6),(10,-1)}

f={(-1,2),(0,4),(2,-4),(5,6),(10,0)}

f=[(1,2),(3,4),(5,6),(8,6)(10,6)}

f={(-1,2),(0,-4),(2,-4),(5,6),(10,2)}

Multiple Choice

5. Which of these is a one to one function?

• f={(1,2),(3,4)(5,6),(8,6),(10,-1)}

• f={(-1,2),(0,4),(2,-4),(5,6),(10,0)}

• f=[(1,2),(3,4),(5,6),(8,6)(10,6)}

• f={(-1,2),(0,-4),(2,-4),(5,6),(10,2)}

6. It is a probability distribution that is symmetric about the mean, showing that the data near the mean are more frequent in occurrence than data far from the mean.

Binomial distribution

Normal distribution

Poisson distribution

Hypergeometric distribution

Multiple Choice

6. It is a probability distribution that is symmetric about the mean, showing that the data near the mean are more frequent in occurrence than data far from the mean.

• Binomial distribution

• Normal distribution

• Poisson distribution

• Hypergeometric distribution

7. “An inspector sampled cans from a truckload of canned creamed corn to estimate the total number of worn cans in the truckload. The truck has 580 cases; each case contains 24 cans. The inspector sampled 12 cases at random and all cans in each selected case were inspected.” What sampling method is used in this situation?

Simple Random Sampling

Cluster Sampling

Systematic Sampling

Stratified Sampling

Multiple Choice

7. “An inspector sampled cans from a truckload of canned creamed corn to estimate the total number of worn cans in the truckload. The truck has 580 cases; each case contains 24 cans. The inspector sampled 12 cases at random and all cans in each selected case were inspected.” What sampling method is used in this situation?

• Simple Random Sampling

• Cluster Sampling

• Systematic Sampling

• Stratified Sampling

8. Which of the following is an example of Interval data?

Weekly Food Spending

Temperature in Fahrenheit

Height of a random basketball player 

Service Quality rating

Multiple Choice

8. Which of the following is an example of Interval data?

• Weekly

  Food Spending

• Temperature

  in Fahrenheit

• Height

  of a random basketball player

• Service

  Quality rating

9. What is the total area under the normal curve?

Fill in the Blank

9. What is the total area under the normal curve?

10. Which of the following is not an example of a Bernoulli random variable (Binomial random variable)?

a.      the number of people who pre-register for an engineering class

b.      whether or not the next person in the checkout at a grocer spends more than P500

c.      flipping a coin

d.      whether or not a light bulb works

Multiple Choice

10. Which of the following is not an example of a Bernoulli random variable (Binomial random variable)?

• the number of people who pre-register for an engineering class

• whether or not the next person in the checkout at a grocer spends more than P500

• flipping a coin

• whether or not a light bulb works

Average Round

30 seconds

1. If f(x)=x²-3x+8, what is the value of f(x) when x=2?

6

8

10

12

Multiple Choice

1. If f(x)=x²-3x+8, what is the value of f(x) when x=2?

• 6

• 8

• 10

• 12

2. The variance of a certain random variable is 2.29. What is the standard deviation? Round your answer to the nearest four decimal places.

Fill in the Blank

2. The variance of a certain random variable is 2.29. What is the standard deviation? Round your answer to the nearest four decimal places.

3. The z-score tells how many standard deviations from the mean a certain score is. A set of Economics Final Exam Grades are normally distributed with a mean of 65 and a standard deviation of 12. Find a z-score for a grade of 62. Round your answer to the nearest two decimal places. 

Fill in the Blank

3. The z-score tells how many standard deviations from the mean a certain score is. A set of Economics Final Exam Grades are normally distributed with a mean of 65 and a standard deviation of 12. Find a z-score for a grade of 62. Round your answer to the nearest two decimal places.

4. It is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time.

Fill in the Blank

4. It is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time.

5. It is a type of annuity where periodic payments are made at the beginning of payment intervals.

Fill in the Blank

5. It is a type of annuity where periodic payments are made at the beginning of payment intervals.

6. TRUE OR FALSE. Binomial distribution is a DISCRETE probability distribution.

Fill in the Blank

6. TRUE OR FALSE. Binomial distribution is a DISCRETE probability distribution.

7. Which of the following equations is incorrect?

ln 4+ ln 6 = ln 24

log 7 + log 5 = log 12

(log_3) 12 - (log_3) 6 = (log_3) 2

ln 15 - ln 5 = ln 3

Multiple Choice

7. Which of the following equations is incorrect?

• ln 4+ ln 6 = ln 24

• log 7 + log 5 = log 12

• (log_3)12 - (log_3) 6 = (log_3) 2

• ln 15 - ln 5 = ln 3

8. Using the standard normal probability table, what is P(Z>-0.31) ? Round your answer to the nearest four decimal places.

Fill in the Blank

8. Using the standard normal probability table, what is P(Z>-0.31) ? Round your answer to the nearest four decimal places.

9. A diagram in rows and columns showing the veracity or falsity of a proposition.

Fill in the Blank

9. A diagram in rows and columns showing the veracity or falsity of a proposition

10. Find the mean of a binomial random variable with n=6 and P=0.13. Round your answer to the nearest two decimal places. 

Fill in the Blank

10. Find the mean of a binomial random variable with n=6 and P=0.13. Round your answer to the nearest two decimal places.

Difficult Round

1 minute

1. If f(x)= 1/(x+4) and g(x)= x²-4, then what is f(g(-2))?

Fill in the Blank

1. If f(x)= 1/(x+4) and g(x)= x²-4, then what is f(g(-2))?

2. Light bulbs are tested for their life-span. It is found that 17% of the light bulbs are rejected. A random sample of 25 bulbs is taken from stock and tested. The random variable X is the number of bulbs that a rejected. Find the probability that exactly 4 bulbs in the samples are rejected. Round your answer to the nearest four decimal places.

Fill in the Blank

2. Light bulbs are tested for their life-span. It is found that 17% of the light bulbs are rejected. A random sample of 25 bulbs is taken from stock and tested. The random variable X is the number of bulbs that are rejected. Find the probability that exactly 4 bulbs in the samples are rejected. Round your answer to the nearest four decimal places.

3. The number of visitors to a webserver per minute follows a Poisson distribution. If the average number of visitors per minute is 8, what is the probability that there are exactly 2 visitors in 30 seconds? Round your answer to the nearest three decimal places.

Fill in the Blank

3. The number of visitors to a webserver per minute follows a Poisson distribution. If the average number of visitors per minute is 8, what is the probability that there are exactly 2 visitors in 30 seconds? Round your answer to the nearest three decimal places.

4. The inverse of f(x)=3x-5  is f^-1(x) = (x+5)/3. What is f composed with f inverse of x?

Fill in the Blank

4. The inverse of f(x)=3x-5 is f^-1(x) = (x+5)/3. What is f composed with f inverse of x?

5. Using the standard normal probability table, find P(0.12<Z<2.77). Round your answer to the nearest four decimal places.

Fill in the Blank

5. Using the standard normal probability table, find  $P\left(0.12\le Z<2.77\right)$ . Round your answer to the nearest four decimal places.

- END of Quiz -

Congratulations to all the participants!