# NAT 2023 Reviewer

## Quiz by RODOLFO MANACHO

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- Q1
It is a variable being measured to produce numerical observations associated with the random outcomes of a chance experiment.

fixed variable

dependent variable

independent variable

random variable

60s - Q2
Which of the following is a discrete random variable?

the number of patients in a hospital

the average weight of female athletes

the average amount of electricity consumed

the amount of paint used in repainting a building

60s - Q3
What are the possible values of a random variable when a coin is tossed once?

Tail (T) and Head (H)

The pair of even number of dots (2,2),(2,4),(2,6),(4,2),(4,4), (4,6),(6,2),(6,4) and (6,6)

Tail and Tail (TT), and Head and Head (HH)

The number of dots 1,2,3,4,5,6

60s - Q4
Which is a discrete probability distribution?

60s - Q5
A fair coin is tossed three times and the sequence of heads (H) and tails (T) isobserved. What is the probability that no heads will appear?

3/8

5/8

1/8

2/3

60s - Q6
The expected value of a random variable is the _________.

mean value over an infinite number of observations of the variable.

most common value over an infinite number of observations of the variable.

largest value that will ever occur.

value that has the highest probability of occurring.

60s - Q7
Cardo sells a maximum of 3 tickets per customer. Let T be the number of tickets sold to a random customer. Which probability value would satisfy the given probability distribution? Below is the probability distribution of T.

0.19

0.16

0.17

0.18

60s - Q8
What is the mean and variance of the probability distribution?

1.67

1.66

1.65

1.64

60s - Q9
What is the variance of the probability distribution?

2.20

2.21

2.19

2.18

60s - Q10
What would be the best interpretation you can create given the mean of the probabilitydistribution?

A group of 10 customers will purchase exactly 29 tickets.

Most customers will purchase 3 tickets.

If we look at a large number of customers, then each customer, on the average, will have purchased about 1.66 tickets.

Cardo can expect to have more tickets sold.

60s - Q11
What is the first step in finding the variance of a discrete probability distribution?

Find the mean of the probability distribution

Multiply the square of the difference of X and the mean by each value of the random variable.

Calculate the standard deviation

Subtract the mean from each value of the random variable X

60s - Q12
Which statement is NOT true about the variance of a discrete random variable?

High variance indicates that the data points are very spread out around the mean.

It measures how far apart the elements of the set are spread out

It tells the average of the items in a discrete probability distribution

Variance is always nonnegative.

60s - Q13
A local club plans to investP10,000 to host a basketball game. They expect to sell tickets worth P15,000. But if it rains on the day of the game, they won't sell any tickets, and the club will lose all the money invested. If the weather forecast for the day of the game is 20% possibility of rain, is this a good investment?

Yes, because theexpected value is negative P2,000

Yes, because the expected value is positive P2,000

No, because the expected value is positive P2,000

No, because the expected value is negative P2,000

60s - Q14
Which of the following is NOT a property of a normal curve?

It is divided into positive 2 and negative 2 standard deviations

The curve is symmetric about thecenter.

The mean, median, and mode have the same value and are located at the same point.

The total area under it is 1.

60s - Q15
The area under the part of normal curve in the standard normal distribution that lies within 2 standard deviations of the mean is ____?

95%

99.7%

68%

100%

60s