Probability and Statistics Applications MCQ Test: Probability and Statistics Applications MCQs - Practice Questions
1. If the variance of a dataset is 25 and there are 5 data points, what is the standard deviation?
2. If the probability of event A is 0.3 and the probability of event B is 0.5, what is the probability of either event A or event B occurring?
3. In a normal distribution, what percentage of data falls within two standard deviations of the mean?
4. If the mean of a dataset is 50 and the z-score of a data point is -2, what is the value of the data point?
5. A fair six-sided die is rolled. What is the probability of rolling a 5 or a 6?
6. A coin is flipped three times. What is the probability of getting exactly two tails?
7. In a survey, 40% of respondents chose option A, 30% chose option B, and the rest chose option C. What is the probability that a randomly selected respondent chose option C?
8. The IQ scores of a population follow a normal distribution with a mean of 100 and a standard deviation of 15. What percentage of the population has an IQ score above 130?
9. The height of a group of students follows a normal distribution with a mean of 160 cm and a standard deviation of 10 cm. What percentage of students have a height between 150 cm and 170 cm?
10. The average time taken to complete a task is 30 minutes with a standard deviation of 5 minutes. What is the probability that a randomly selected task takes more than 35 minutes to complete?
11. If the median of a dataset is 10, and there are 7 data points, what is the value of the fourth data point?
12. A manufacturing process produces bolts with a mean length of 20 cm and a standard deviation of 2 cm. If the lengths follow a normal distribution, what percentage of bolts have a length less than 18 cm?
13. If a bag contains 10 red and 5 blue marbles, what is the probability of drawing a red marble followed by a blue marble without replacement?
14. In a group of 30 students, 20 are girls. What is the probability of randomly selecting a girl from the group?
15. A bag contains 4 red, 3 blue, and 5 green marbles. If two marbles are drawn without replacement, what is the probability of getting two green marbles?
16. In a survey, 60% of respondents prefer option A, 20% prefer option B, and the rest prefer option C. What is the probability that a randomly selected respondent prefers option C?
17. If the interquartile range of a dataset is 12, and the first quartile is 25, what is the third quartile?
18. A coin is flipped four times. What is the probability of getting at least three heads?
19. If a bag contains 8 red, 4 blue, and 2 green balls, what is the probability of drawing a green ball?
20. The average weight of a group of students is 150 pounds with a standard deviation of 20 pounds. If the data follows a normal distribution, what percentage of students weigh more than 170 pounds?
21. A random sample of 100 students has an average test score of 75 with a standard deviation of 10. What is the standard error of the mean?
22. If the probability of event A is 0.6 and the probability of event B is 0.7, what is the probability of either event A or event B occurring?
23. If the mean of a dataset is 15 and there are 5 data points, what is the sum of the data points?
24. If the correlation coefficient between two variables is -0.8, what does this indicate about the relationship between the variables?
25. A deck of cards is shuffled. What is the probability of drawing a face card (king, queen, or jack)?
26. The heights of a group of students follow a normal distribution with a mean of 170 cm and a standard deviation of 8 cm. What percentage of students have a height above 180 cm?
27. If the probability of event A is 0.5 and the probability of event B is 0.3, what is the probability of both events A and B not occurring?
28. In a survey, 25% of respondents preferred option A, 30% preferred option B, and the rest preferred option C. What is the probability that a randomly selected respondent did not choose option C?
29. In a set of data, the range is 15, and there are 5 data points. What is the difference between the maximum and minimum values?
30. A bag contains 6 red, 4 blue, and 3 green balls. If two balls are drawn without replacement, what is the probability of getting one red and one blue ball?
31. A box contains 5 red, 3 blue, and 2 green balls. If two balls are drawn with replacement, what is the probability of both being green?
32. A bag contains 8 red, 5 blue, and 4 green balls. If three balls are drawn with replacement, what is the probability of getting exactly two red balls?
33. In a deck of cards, what is the probability of drawing an ace or a king?
34. A deck of cards is shuffled. What is the probability of drawing an ace or a king?
35. A bag contains 5 red, 4 blue, and 6 green marbles. If two marbles are drawn without replacement, what is the probability of getting two blue marbles?
36. If a fair six-sided die is rolled five times, what is the probability of getting exactly one 6?
37. The height of a group of students follows a normal distribution with a mean of 160 cm and a standard deviation of 10 cm. What percentage of students have a height above 170 cm?
38. In a bag of colored marbles, there are 5 red, 3 blue, and 2 green marbles. What is the probability of drawing a blue marble?
39. In a survey, 60% of respondents preferred option A, and 40% preferred option B. What is the odds in favor of choosing option A?
40. A six-sided die is rolled. What is the probability of rolling an even number?