Statistics and Probability Quiz for Q3

Which of the following statements correctly describes a probability distribution?

• A probability distribution must have exactly two outcomes.

• The probability of any outcome can be greater than 1.

• The sum of all probabilities must be less than 1.

• The sum of all probabilities must be exactly 1.

A lottery has tickets numbered from 1 to 200, and a winning ticket is chosen randomly. What is the probability that the winning ticket has a number divisible by 5?

• 0.10

• 0.20

• 0.50

• 0.80

The variance of a discrete random variable measures ____.

• The expected value of the variable

• The spread of possible outcomes around the mean.

• The most frequent outcome

• The number of possible outcomes

A store gives a ₱600 reward to premium customers with a 40% chance and a ₱300 reward to regular customers with a 60% chance. What is the expected reward?

• ₱360

• ₱480

• ₱420

• ₱600

In a normal distribution, the mean, median, and mode are always ____.

• Equal.

• Different but close in value

• Located at different parts of the distribution

• Undefined

The height of adult men in a city is normally distributed with a mean of 170 cm and a standard deviation of 8 cm. What percentage of men are taller than 178 cm?

• 84.13%

• 15.87%

• 68.27%

• 30.85%

What happens to the standard error of the sample mean when the sample size increases?

• It increases

• It decreases.

• It remains the same

• It becomes equal to the population standard deviation

The average math test score in a university is 80 with a standard deviation of 12. If 36 students are randomly selected, what percentage of students score below 82 in the sampling distribution?

• 69.15%

• 84.13%

• 75.00%

• 90.00%

The standard error of the sample proportion gets smaller when ____.

• The sample size decreases

• The sample size increases.

• The population proportion is close to 0.5

• The mean is greater than the proportion

10. A recent study shows that 40% of customers prefer digital payment. If a random sample of 150 customers is taken, what is the probability that the sample proportion of digital payment users will be at most 0.35? Assume that the sample follows a normal distribution.

• 0.1056

• 0.1446

• 0.1870

• 0.2236