#1. A machine produces bolts with a mean diameter of 12.00 mm and a standard deviation of 0.08 mm. Assuming diameters are normally distributed, what percentage of bolts will have diameters between 11.84 mm and 12.16 mm?
#2. The heights of adult males in a population are normally distributed with a mean of 175 cm and a standard deviation of 7 cm. What height corresponds to the 95th percentile? Use z = 1.645 for the 95th percentile.
#3. Test scores are normally distributed with a mean of 82 and a standard deviation of 6. What is the probability that a randomly selected score is greater than 88?
#4. A process produces parts with weights normally distributed with μ = 50 g and σ = 4 g. What is the z-score for a part weighing 58 g?
#5. For a standard normal distribution, P(Z < 1.28) = 0.8997. What is P(Z > 1.28)?
#6. A quality control inspector checks 15 items from a batch where 10% are defective. What is the expected number of defective items in the sample?
#7. In a binomial experiment with n = 8 trials and p = 0.25, what is the probability of exactly 2 successes?
#8. A fair coin is flipped 20 times. What is the standard deviation of the number of heads?
#9. A student guesses on a 10-question true/false quiz. What is the probability of getting at least 8 correct?
#10. A production line has a 3% defect rate. In a sample of 200 items, what is the expected number of defective items?
#11. A call center receives an average of 8 calls per hour. Using the Poisson distribution, what is the probability of receiving exactly 5 calls in an hour?
#12. Traffic accidents occur at an intersection at a rate of 2 per week. What is the probability of exactly 4 accidents occurring in a given week?
#13. A manufacturing process produces defects at a rate of 0.5 per 100 meters. What is the expected number of defects in 400 meters?
#14. Emails arrive at a server at an average rate of 12 per minute. What is the variance of the number of emails received per minute?
#15. A rare event occurs on average 0.8 times per day. What is the probability that the event does not occur on a given day?
#16. The time between customer arrivals follows an exponential distribution with a mean of 5 minutes. What is the rate parameter λ?
#17. A light bulb has a mean lifetime of 1000 hours following an exponential distribution. What is the probability that a bulb lasts more than 500 hours?
#18. Machine breakdowns occur at a rate of 0.02 per hour. What is the probability that the machine operates for more than 100 hours without breaking down?
#19. For an exponential distribution with λ = 0.5, what is the variance?
#20. The mean time to failure for a component is 250 hours. Using the exponential distribution, what is the probability of failure within the first 50 hours?
#21. The following data represents daily production quantities: 85, 92, 78, 95, 88, 90, 82. What is the sample mean?
#22. For the dataset: 4, 7, 9, 12, 15, 18, 21, 24, what is the median?
#23. A dataset has values: 23, 27, 27, 31, 35, 27, 42. What is the mode?
#24. The sample variance of a dataset is 49. What is the sample standard deviation?
#25. For a dataset with Q1 = 35 and Q3 = 65, what is the interquartile range (IQR)?
#26. A sample of 49 observations has a mean of 120 and a known population standard deviation of 14. Using z = 1.96 for 95% confidence, what is the margin of error?
#27. A 90% confidence interval for a population mean is (45, 55). What is the sample mean?
#28. A sample of 81 items has a mean of 250 and a standard deviation of 27. What is the standard error of the mean?
#29. An engineer wants to estimate a population proportion with 95% confidence and a margin of error of 0.04. Using p = 0.5 and z = 1.96, what is the minimum required sample size?
#30. A sample of 36 measurements yields a mean of 72 and a population standard deviation of 12. What is the 95% confidence interval for the population mean? (z = 1.96)
#31. A z-test produces a test statistic of z = 2.15. For a two-tailed test at α = 0.05 (critical values ±1.96), what is the conclusion?
#32. In a hypothesis test, the probability of a Type II error is 0.12. What is the power of the test?
#33. A sample of 50 items has a mean of 105. Testing H₀: μ = 100 vs H₁: μ ≠ 100 with σ = 10, what is the z-test statistic?
#34. A p-value of 0.08 is obtained from a hypothesis test. At α = 0.05, what is the correct conclusion?
#35. For a one-tailed test at α = 0.01, what is the critical z-value?
#36. A regression equation is ŷ = 4.5x + 12. What is the predicted value of y when x = 8?
#37. In a regression analysis, SST = 500 and SSE = 125. What is the coefficient of determination R²?
#38. A regression line has slope 3.2 with x̄ = 5 and ȳ = 24. What is the y-intercept?
#39. For the regression equation ŷ = 2.1x + 8, an observed point is (5, 20). What is the residual?
#40. A regression analysis with 20 data points has SSE = 360. What is the standard error of the estimate?
#41. Given Cov(X, Y) = 18, σX = 3, and σY = 9, what is the correlation coefficient?
#42. If R² = 0.81 and the relationship is negative, what is the correlation coefficient r?
#43. Which correlation coefficient indicates the strongest linear relationship?
#44. Two variables have σX = 5, σY = 8, and r = 0.6. What is the covariance Cov(X, Y)?
#45. A study reports r = 0.95 between advertising spending and sales. Which statement is most accurate?
#46. For events A and B, P(A) = 0.5, P(B) = 0.4, and P(A ∩ B) = 0.2. What is P(A | B)?
#47. Events C and D are independent with P(C) = 0.3 and P(D) = 0.6. What is P(C ∩ D)?
#48. For mutually exclusive events E and F, P(E) = 0.25 and P(F) = 0.45. What is P(E ∪ F)?
#49. P(A) = 0.6 and P(B | A) = 0.75. What is P(A ∩ B)?
#50. The complement of event G has probability P(G’) = 0.35. What is P(G)?
#51. In how many ways can 6 different books be arranged on a shelf?
#52. A committee of 4 is to be selected from 10 candidates. How many different committees are possible?
#53. A password consists of 3 letters followed by 2 digits. If repetition is allowed, how many passwords are possible?
#54. How many different 5-card hands can be dealt from a standard 52-card deck?
#55. In how many ways can the letters of BOOK be arranged?
#56. Three components in series have reliabilities 0.92, 0.88, and 0.95. What is the system reliability?
#57. Two components in parallel have reliabilities 0.85 and 0.80. What is the system reliability?
#58. A component has a 5% probability of failure. If 4 independent components are used in series, what is the probability that the system works?
#59. For two identical components in parallel, each with reliability 0.90, what is the probability that exactly one component works?
#60. A system needs at least 2 of 3 identical components (reliability 0.80 each) to function. What is the system reliability?
#61. A random variable X has E[X] = 8 and Var(X) = 4. What is E[3X + 2]?
#62. If Var(X) = 9, what is Var(2X – 5)?
#63. X and Y are independent with E[X] = 4 and E[Y] = 7. What is E[XY]?
#64. A game pays $15 with probability 0.2, $5 with probability 0.5, and $0 with probability 0.3. What is the expected payout?
#65. If E[X] = 6 and E[X²] = 42, what is Var(X)?
#66. A population has μ = 100 and σ = 20. For samples of size 64, what is the standard error of the mean?
#67. According to the Central Limit Theorem, for large samples from any population, the distribution of sample means is approximately:
#68. A population proportion is p = 0.40. For samples of size 100, what is the standard deviation of the sampling distribution of p̂?
#69. If individual observations have σ = 15, how large must the sample be for the standard error to be 3?
#70. A sample of 36 observations is drawn from a population with σ = 18. What is P(X̄ > μ + 3)?
#71. A chi-square goodness-of-fit test has 5 categories. What are the degrees of freedom?
#72. In a chi-square test of independence with a 4×3 contingency table, what are the degrees of freedom?
#73. In one-way ANOVA with 5 groups and 50 total observations, what are the between-groups degrees of freedom?
#74. For a chi-square test, the observed frequency is 45 and expected frequency is 50. What is this cell’s contribution to the chi-square statistic?
#75. ANOVA produces MSB = 120 and MSW = 30. What is the F-statistic?
#76. A random variable X follows a continuous uniform distribution on [10, 30]. What is E[X]?
#77. For a uniform distribution on [0, 8], what is the variance?
#78. A bus arrives uniformly between 0 and 15 minutes after each hour. What is the probability of waiting more than 10 minutes?
#79. For X ~ Uniform(5, 25), what is P(10 < X < 20)?
#80. The PDF of a continuous uniform distribution on [a, b] is 0.05. What is (b – a)?
#81. A sample of 16 observations has s = 8. What is the standard error for estimating the population mean?
#82. For a t-test with n = 25 observations, what are the degrees of freedom?
#83. A sample of 10 yields x̄ = 45 and s = 6. Testing H₀: μ = 42, what is the t-statistic?
#84. As the degrees of freedom increase, the t-distribution approaches which distribution?
#85. A two-sample t-test uses samples of sizes 12 and 18. With pooled variance, what are the degrees of freedom?
#86. A distribution has mean = 45, median = 50, and mode = 55. This distribution is:
#87. For a perfectly symmetric distribution, Pearson’s coefficient of skewness equals:
#88. A dataset has mean 80, median 75, and standard deviation 10. What is Pearson’s coefficient of skewness?
#89. Income distributions are typically:
#90. If mean < median, the distribution is:
#91. In a dataset of 40 values, the 25th percentile corresponds to approximately which position when data is sorted?
#92. If Q1 = 30, Q2 = 45, and Q3 = 60, what is the IQR?
#93. Using the 1.5×IQR rule, if Q1 = 20 and Q3 = 50, what is the upper fence for outlier detection?
#94. The median of a dataset is also called the:
#95. For the sorted data: 2, 5, 8, 11, 14, 17, 20, 23, what is Q1?
#96. The coefficient of variation for a dataset with mean 50 and standard deviation 10 is:
#97. A 99% confidence interval will be _____ than a 95% confidence interval from the same data.
#98. The geometric mean of 4, 8, and 32 is:
#99. Three measurements have values 15, 25, and 35 with weights 1, 2, and 2. What is the weighted mean?
#100. Using Chebyshev’s inequality, at least what percentage of data falls within 4 standard deviations of the mean?
