Numeracy Assessment for Statistics

Which of the following statements best describes a random variable?

• It is a variable that can only take on discrete values.

• It is a variable that can take on any value within a certain range.

• It is a variable whose value is determined by chance or random variation.

• It is a variable that is completely independent of other variables in a system.

Which of the following is an example of a discrete random variable?

• The time it takes to finish a 10-item test.

• The average stock price of JFC in one year.

• The population size of a country.

• The maturity value of a loan.

A shipment of five cellphones contains two that are slightly defective. A retailer receives three of these cellphones at random. Let X be the random variable representing the number of slightly defective cellphones that the retailer receives. Which of the following is NOT a possible value of X?

• 0

• 1

• 2

• 3

Which of the following statements is TRUE about the possible value of the probability of the random variable?

• The sum of all probability values is Greater than 1.

• The sum of all probability values is 1.

• The sum of all probability values is greater than 0 but less than 1.

• The sum of all probability values is between 0 and ½.

Lucky Store is giving away 20 lucky bags for their first anniversary. Ten (10) bags contain PhP50, seven bags contain PhP100, eight bags contain PhP200, and five bags contain PhP500. Which table represents the discrete probability distribution of the data above?

• 
• 
• 
• 

Which of the following statements best describes the probability histogram given?

• The mean is equal to 6, and it implies that the distance of the element from the mean in either direction is 3.

• The mean is equal to 6, and it implies that the distance of the element from the mean in either direction is 6.

• The mean is equal to 3, and it implies that the distance of the element from the mean in either direction is 3.

• The mean is equal to 3, and it implies that the distance of the element from the mean in either direction is 6.

There are three balls numbered 2, 4, and 6 in a jar. One ball is selected at random, its number is noted, and then returned to the jar. If this experiment is done many times, which of the following is the mean of the numbers on the ball?

• 2

• 4

• 6

• 12

The mean of a discrete random variable X is 5. Which of the following statements is the correct interpretation of this value?

• The most common value over many repeats of the experiment is 5.

• Two of the values of X are 4 and 6 with equal probabilities of occurrence.

• The value of the random variable X with the highest probability value is 5.

• The weighted average value for X over many repeats of the experiment is 5.

Forty students were asked how much their daily school allowance is. Below is the distribution table of their answers. PhP20.00 15 PhP50.00 10 PhP70.00 10 PhP100.00 5 Let X be the random variable representing the student’s daily allowance. X is 1 for PhP20.00, 2 is for PhP50.00, 3 is for PhP70.00, and 4 is for PhP100.00. What is the mean and variance of the student’s daily school allowance?

• Mean = 1.95 and Variance = 0.69

• Mean = 2.25 and Variance = 0.75

• Mean = 2.5 and Variance = 0.875

• Mean = 2.75 and Variance = 1.0

Which of the following best describes the mean of a normal random variable?

• The mean is the point at which the distribution is centered.

• The mean is the highest point of the distribution.

• The mean is the average of all the observations.

• The mean is the point where the tails of the distribution start.