What are the possible values of a random variable when a coin is tossed once?

• Tail (T) and Head (H)

• The number of dots 1,2,3,4,5,6

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

• 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)

Answer explanation

The possible values of a random variable when a coin is tossed once are Tail (T) and Head (H), making option A the correct choice.

What is the first step in finding the variance of a discrete probability distribution?

• Calculate the standard deviation

• Find the mean of the probability distribution

• Subtract the mean from each value of the random variable X

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

Answer explanation

The first step in finding the variance of a discrete probability distribution is to find the mean of the probability distribution.

Which of the following is NOT a property of a normal curve?

• The total area under it is 1.

• The curve is symmetric about the center.

• It is divided into positive 2 and negative 2 standard deviations

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

Answer explanation

The correct choice is C because a normal curve is divided into positive and negative standard deviations, not specifically 2 and -2 standard deviations.

Tags

CCSS.HSS.ID.A.4

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

• 1/8

• 3/8

• 5/8

• 2/3

Answer explanation

The probability of getting tails in one toss is 1/2. Since the coin is fair, the probability of getting tails in three tosses is (1/2)^3 = 1/8. Therefore, the probability of no heads appearing is 1/8.

Which of the following illustrates a systematic sampling method?

• A researcher conducted a survey of 50 randomly selected workers from each of these categories: high school graduate, with undergraduate degrees, with master’s degree, and with doctoral degree.

• A researcher interviewed all freshmen in each of 15 randomly selected public schools in Surigao del Norte.

• A researcher doing a research work on students’ reaction of the newly implemented curriculum and interviewed every 10th student entering the gate.

• A researcher selected a sample of n = 120 from a population 850 using the Table of Random Numbers.

Answer explanation

Answer Explanation highlighting the correct choice of a systematic sampling method

Tags

CCSS.HSS.IC.B.3

The expected value of a random variable is the

• largest value that will ever occur.

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

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

• value that has the highest probability of occurring.

Answer explanation

The expected value of a random variable is the mean value over an infinite number of observations of the variable, making option B the correct choice.

Tags

CCSS.HSS.MD.A.2

The area under the part of normal curve in the standard normal distribution that lies within 2 standard deviations of the mean is

• 68%

• 95%

• 99.7%

• 100%

Answer explanation

The area under the part of normal curve within 2 standard deviations of the mean in the standard normal distribution is 95%, which corresponds to choice B.

Tags

CCSS.HSS.ID.A.4

What would be the best interpretation you can create given the mean of the probability distribution?

• Most customers will purchase 3 tickets.

• Cardo can expect to have more tickets sold.

• A group of 10 customers will purchase exactly 29 tickets.

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

Answer explanation

The best interpretation of the mean of the probability distribution is that if we look at a large number of customers, then each customer, on average, will have purchased about 1.66 tickets.

Tags

CCSS.HSS.MD.A.2

What is the variance of the probability distribution?

• 2.18

• 2.19

• 2.20

• 2.21

Answer explanation

The correct answer is A. 2.18 as it matches the variance of the probability distribution provided in the question.

A randomly selected sample of 400 students at a university with 15-week semesters was asked whether or not they think the semester should be shortened to 14 weeks (with longer classes). Forty-six percent (46%) of the 400 students surveyed answered "yes." Which one of the following statements about the number 46% is correct?

• It is a sample statistic

• It is a random variable

• It is a population parameter

• It is a quantitative discrete variable

Answer explanation

The correct choice is C because 46% is a population parameter, representing the proportion of all students at the university who think the semester should be shortened.