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Probability and Statistics –
Medium Difficulty
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LET’S PRACTICE!
#1. For data set [39, 38, 37, 36, 38], what is the arithmetic mean?
#2. If X~Binomial(n=9, p=0.5), find P(X=3).
#3. For standard normal Z, estimate P(Z ≤ 0.5).
#4. Given P(A)=0.5, P(B)=0.3, and P(A∩B)=0.12, find P(A|B).
#5. A discrete random variable has P(X=3)=0.111, P(X=6)=0.333, P(X=2)=0.444, P(X=5)=0.111. Compute E[X].
#6. If T is exponential with rate λ=0.5, find P(T ≤ 1).
#7. A process has population standard deviation 4. For sample size n=27, what is the standard error of the sample mean?
#8. For X~N(μ=58, σ=7), find the z-score of x=65.
#9. Given P(A)=0.45, P(B|A)=0.8, and P(B|A^c)=0.2, compute P(A|B).
#10. If X is uniformly distributed on [5, 16], what is Var(X)?
#11. For data set [37, 27, 39, 11, 10], what is the arithmetic mean?
#12. If X~Binomial(n=7, p=0.4), find P(X=2).
#13. For standard normal Z, estimate P(Z ≤ -1.0).
#14. Given P(A)=0.3, P(B)=0.5, and P(A∩B)=0.12, find P(A|B).
#15. A discrete random variable has P(X=6)=0.4, P(X=6)=0.1, P(X=4)=0.3, P(X=4)=0.2. Compute E[X].
#16. If T is exponential with rate λ=0.8, find P(T ≤ 1).
#17. A process has population standard deviation 8. For sample size n=33, what is the standard error of the sample mean?
#18. For X~N(μ=83, σ=5), find the z-score of x=78.
#19. Given P(A)=0.55, P(B|A)=0.8, and P(B|A^c)=0.3, compute P(A|B).
#20. If X is uniformly distributed on [10, 23], what is Var(X)?
#21. For data set [35, 29, 32, 30, 35], what is the arithmetic mean?
#22. If X~Binomial(n=7, p=0.5), find P(X=2).
#23. For standard normal Z, estimate P(Z ≤ 1.0).
#24. Given P(A)=0.6, P(B)=0.4, and P(A∩B)=0.168, find P(A|B).
#25. A discrete random variable has P(X=1)=0.2, P(X=4)=0.1, P(X=1)=0.3, P(X=4)=0.4. Compute E[X].
#26. If T is exponential with rate λ=0.5, find P(T ≤ 3).
#27. A process has population standard deviation 6. For sample size n=22, what is the standard error of the sample mean?
#28. For X~N(μ=67, σ=7), find the z-score of x=74.
#29. Given P(A)=0.55, P(B|A)=0.6, and P(B|A^c)=0.3, compute P(A|B).
#30. If X is uniformly distributed on [10, 14], what is Var(X)?
#31. For data set [38, 30, 26, 16, 13], what is the arithmetic mean?
#32. If X~Binomial(n=6, p=0.5), find P(X=2).
#33. Given P(A)=0.5, P(B)=0.5, and P(A∩B)=0.2, find P(A|B).
#34. A discrete random variable has P(X=5)=0.1, P(X=5)=0.3, P(X=1)=0.2, P(X=4)=0.4. Compute E[X].
#35. If T is exponential with rate λ=0.4, find P(T ≤ 2).
#36. A process has population standard deviation 8. For sample size n=16, what is the standard error of the sample mean?
#37. For X~N(μ=73, σ=14), find the z-score of x=87.
#38. Given P(A)=0.55, P(B|A)=0.8, and P(B|A^c)=0.2, compute P(A|B).
#39. If X is uniformly distributed on [10, 19], what is Var(X)?
#40. For data set [25, 26, 38, 11, 21], what is the arithmetic mean?
#41. If X~Binomial(n=7, p=0.4), find P(X=3).
#42. Given P(A)=0.3, P(B)=0.3, and P(A∩B)=0.072, find P(A|B).
#43. A discrete random variable has P(X=5)=0.273, P(X=6)=0.364, P(X=6)=0.273, P(X=4)=0.091. Compute E[X].
#44. If T is exponential with rate λ=0.2, find P(T ≤ 4).
#45. A process has population standard deviation 7. For sample size n=29, what is the standard error of the sample mean?
#46. For X~N(μ=72, σ=13), find the z-score of x=59.
#47. Given P(A)=0.55, P(B|A)=0.7, and P(B|A^c)=0.3, compute P(A|B).
#48. If X is uniformly distributed on [7, 16], what is Var(X)?
#49. For data set [39, 36, 33, 10, 21], what is the arithmetic mean?
#50. If X~Binomial(n=10, p=0.5), find P(X=3).
#51. Given P(A)=0.5, P(B)=0.2, and P(A∩B)=0.07, find P(A|B).
#52. A discrete random variable has P(X=3)=0.167, P(X=4)=0.167, P(X=4)=0.167, P(X=2)=0.5. Compute E[X].
#53. If T is exponential with rate λ=0.8, find P(T ≤ 4).
#54. A process has population standard deviation 9. For sample size n=27, what is the standard error of the sample mean?
#55. For X~N(μ=51, σ=5), find the z-score of x=56.
#56. Given P(A)=0.45, P(B|A)=0.8, and P(B|A^c)=0.4, compute P(A|B).
#57. If X is uniformly distributed on [9, 19], what is Var(X)?
#58. For data set [21, 20, 11, 32, 34], what is the arithmetic mean?
#59. Given P(A)=0.5, P(B)=0.5, and P(A∩B)=0.15, find P(A|B).
#60. A discrete random variable has P(X=5)=0.143, P(X=5)=0.571, P(X=5)=0.143, P(X=1)=0.143. Compute E[X].
#61. If T is exponential with rate λ=0.4, find P(T ≤ 4).
#62. A process has population standard deviation 9. For sample size n=29, what is the standard error of the sample mean?
#63. For X~N(μ=99, σ=14), find the z-score of x=113.
#64. Given P(A)=0.6, P(B|A)=0.7, and P(B|A^c)=0.4, compute P(A|B).
#65. For data set [29, 23, 24, 34, 23], what is the arithmetic mean?
#66. If X~Binomial(n=6, p=0.4), find P(X=3).
#67. For standard normal Z, estimate P(Z ≤ 2.0).
#68. Given P(A)=0.3, P(B)=0.2, and P(A∩B)=0.048, find P(A|B).
#69. A discrete random variable has P(X=4)=0.182, P(X=2)=0.273, P(X=2)=0.364, P(X=4)=0.182. Compute E[X].
#70. If T is exponential with rate λ=0.4, find P(T ≤ 3).
#71. A process has population standard deviation 9. For sample size n=24, what is the standard error of the sample mean?
#72. For X~N(μ=60, σ=11), find the z-score of x=49.
#73. Given P(A)=0.6, P(B|A)=0.7, and P(B|A^c)=0.2, compute P(A|B).
#74. If X is uniformly distributed on [12, 17], what is Var(X)?
#75. For data set [18, 24, 19, 15, 27], what is the arithmetic mean?
#76. A discrete random variable has P(X=3)=0.4, P(X=2)=0.2, P(X=6)=0.3, P(X=5)=0.1. Compute E[X].
#77. For X~N(μ=56, σ=9), find the z-score of x=47.
#78. If X is uniformly distributed on [9, 14], what is Var(X)?
#79. For data set [34, 25, 35, 27, 22], what is the arithmetic mean?
#80. If X~Binomial(n=6, p=0.5), find P(X=5).
#81. Given P(A)=0.3, P(B)=0.2, and P(A∩B)=0.036, find P(A|B).
#82. A discrete random variable has P(X=4)=0.1, P(X=1)=0.3, P(X=1)=0.3, P(X=5)=0.3. Compute E[X].
#83. If T is exponential with rate λ=0.2, find P(T ≤ 1).
#84. A process has population standard deviation 5. For sample size n=17, what is the standard error of the sample mean?
#85. For X~N(μ=71, σ=15), find the z-score of x=56.
#86. If X is uniformly distributed on [12, 19], what is Var(X)?
#87. For data set [38, 13, 17, 29, 20], what is the arithmetic mean?
#88. If X~Binomial(n=8, p=0.5), find P(X=3).
#89. Given P(A)=0.5, P(B)=0.3, and P(A∩B)=0.09, find P(A|B).
#90. A discrete random variable has P(X=4)=0.333, P(X=2)=0.25, P(X=4)=0.083, P(X=2)=0.333. Compute E[X].
#91. If T is exponential with rate λ=0.2, find P(T ≤ 3).
#92. A process has population standard deviation 7. For sample size n=33, what is the standard error of the sample mean?
#93. For X~N(μ=72, σ=8), find the z-score of x=80.
#94. Given P(A)=0.45, P(B|A)=0.7, and P(B|A^c)=0.4, compute P(A|B).
#95. If X is uniformly distributed on [7, 18], what is Var(X)?
#96. For data set [25, 38, 11, 30, 22], what is the arithmetic mean?
#97. If X~Binomial(n=6, p=0.5), find P(X=3).
#98. For standard normal Z, estimate P(Z ≤ 1.5).
#99. Given P(A)=0.6, P(B)=0.3, and P(A∩B)=0.108, find P(A|B).
#100. A discrete random variable has P(X=3)=0.273, P(X=3)=0.273, P(X=5)=0.182, P(X=2)=0.273. Compute E[X].
#102. For data set [39, 38, 37, 36, 38], what is the arithmetic mean?
#103. If X~Binomial(n=9, p=0.5), find P(X=3).
#104. For standard normal Z, estimate P(Z ≤ 0.5).
#105. Given P(A)=0.5, P(B)=0.3, and P(A∩B)=0.12, find P(A|B).
#106. A discrete random variable has P(X=3)=0.111, P(X=6)=0.333, P(X=2)=0.444, P(X=5)=0.111. Compute E[X].
#107. If T is exponential with rate λ=0.5, find P(T ≤ 1).
#108. A process has population standard deviation 4. For sample size n=27, what is the standard error of the sample mean?
#109. For X~N(μ=58, σ=7), find the z-score of x=65.
#110. Given P(A)=0.45, P(B|A)=0.8, and P(B|A^c)=0.2, compute P(A|B).
#111. If X is uniformly distributed on [5, 16], what is Var(X)?
#112. For data set [37, 27, 39, 11, 10], what is the arithmetic mean?
#113. If X~Binomial(n=7, p=0.4), find P(X=2).
#114. For standard normal Z, estimate P(Z ≤ -1.0).
#115. Given P(A)=0.3, P(B)=0.5, and P(A∩B)=0.12, find P(A|B).
#116. A discrete random variable has P(X=6)=0.4, P(X=6)=0.1, P(X=4)=0.3, P(X=4)=0.2. Compute E[X].
#117. If T is exponential with rate λ=0.8, find P(T ≤ 1).
#118. A process has population standard deviation 8. For sample size n=33, what is the standard error of the sample mean?
#119. For X~N(μ=83, σ=5), find the z-score of x=78.
#120. Given P(A)=0.55, P(B|A)=0.8, and P(B|A^c)=0.3, compute P(A|B).
#121. If X is uniformly distributed on [10, 23], what is Var(X)?
#122. For data set [35, 29, 32, 30, 35], what is the arithmetic mean?
#123. If X~Binomial(n=7, p=0.5), find P(X=2).
#124. For standard normal Z, estimate P(Z ≤ 1.0).
#125. Given P(A)=0.6, P(B)=0.4, and P(A∩B)=0.168, find P(A|B).
#126. A discrete random variable has P(X=1)=0.2, P(X=4)=0.1, P(X=1)=0.3, P(X=4)=0.4. Compute E[X].
#127. If T is exponential with rate λ=0.5, find P(T ≤ 3).
#128. A process has population standard deviation 6. For sample size n=22, what is the standard error of the sample mean?
#129. For X~N(μ=67, σ=7), find the z-score of x=74.
#130. Given P(A)=0.55, P(B|A)=0.6, and P(B|A^c)=0.3, compute P(A|B).
#131. If X is uniformly distributed on [10, 14], what is Var(X)?
#132. For data set [38, 30, 26, 16, 13], what is the arithmetic mean?
#133. If X~Binomial(n=6, p=0.5), find P(X=2).
#134. Given P(A)=0.5, P(B)=0.5, and P(A∩B)=0.2, find P(A|B).
#135. A discrete random variable has P(X=5)=0.1, P(X=5)=0.3, P(X=1)=0.2, P(X=4)=0.4. Compute E[X].
#136. If T is exponential with rate λ=0.4, find P(T ≤ 2).
#137. A process has population standard deviation 8. For sample size n=16, what is the standard error of the sample mean?
#138. For X~N(μ=73, σ=14), find the z-score of x=87.
#139. Given P(A)=0.55, P(B|A)=0.8, and P(B|A^c)=0.2, compute P(A|B).
#140. If X is uniformly distributed on [10, 19], what is Var(X)?
#141. For data set [25, 26, 38, 11, 21], what is the arithmetic mean?
#142. If X~Binomial(n=7, p=0.4), find P(X=3).
#143. Given P(A)=0.3, P(B)=0.3, and P(A∩B)=0.072, find P(A|B).
#144. A discrete random variable has P(X=5)=0.273, P(X=6)=0.364, P(X=6)=0.273, P(X=4)=0.091. Compute E[X].
#145. If T is exponential with rate λ=0.2, find P(T ≤ 4).
#146. A process has population standard deviation 7. For sample size n=29, what is the standard error of the sample mean?
#147. For X~N(μ=72, σ=13), find the z-score of x=59.
#148. Given P(A)=0.55, P(B|A)=0.7, and P(B|A^c)=0.3, compute P(A|B).
#149. If X is uniformly distributed on [7, 16], what is Var(X)?
#150. For data set [39, 36, 33, 10, 21], what is the arithmetic mean?
#151. If X~Binomial(n=10, p=0.5), find P(X=3).
#152. Given P(A)=0.5, P(B)=0.2, and P(A∩B)=0.07, find P(A|B).
#153. A discrete random variable has P(X=3)=0.167, P(X=4)=0.167, P(X=4)=0.167, P(X=2)=0.5. Compute E[X].
#154. If T is exponential with rate λ=0.8, find P(T ≤ 4).
#155. A process has population standard deviation 9. For sample size n=27, what is the standard error of the sample mean?
#156. For X~N(μ=51, σ=5), find the z-score of x=56.
#157. Given P(A)=0.45, P(B|A)=0.8, and P(B|A^c)=0.4, compute P(A|B).
#158. If X is uniformly distributed on [9, 19], what is Var(X)?
#159. For data set [21, 20, 11, 32, 34], what is the arithmetic mean?
#160. Given P(A)=0.5, P(B)=0.5, and P(A∩B)=0.15, find P(A|B).
#161. A discrete random variable has P(X=5)=0.143, P(X=5)=0.571, P(X=5)=0.143, P(X=1)=0.143. Compute E[X].
#162. If T is exponential with rate λ=0.4, find P(T ≤ 4).
#163. A process has population standard deviation 9. For sample size n=29, what is the standard error of the sample mean?
#164. For X~N(μ=99, σ=14), find the z-score of x=113.
#165. Given P(A)=0.6, P(B|A)=0.7, and P(B|A^c)=0.4, compute P(A|B).
#166. For data set [29, 23, 24, 34, 23], what is the arithmetic mean?
#167. If X~Binomial(n=6, p=0.4), find P(X=3).
#168. For standard normal Z, estimate P(Z ≤ 2.0).
#169. Given P(A)=0.3, P(B)=0.2, and P(A∩B)=0.048, find P(A|B).
#170. A discrete random variable has P(X=4)=0.182, P(X=2)=0.273, P(X=2)=0.364, P(X=4)=0.182. Compute E[X].
#171. If T is exponential with rate λ=0.4, find P(T ≤ 3).
#172. A process has population standard deviation 9. For sample size n=24, what is the standard error of the sample mean?
#173. For X~N(μ=60, σ=11), find the z-score of x=49.
#174. Given P(A)=0.6, P(B|A)=0.7, and P(B|A^c)=0.2, compute P(A|B).
#175. If X is uniformly distributed on [12, 17], what is Var(X)?
#176. For data set [18, 24, 19, 15, 27], what is the arithmetic mean?
#177. A discrete random variable has P(X=3)=0.4, P(X=2)=0.2, P(X=6)=0.3, P(X=5)=0.1. Compute E[X].
#178. For X~N(μ=56, σ=9), find the z-score of x=47.
#179. If X is uniformly distributed on [9, 14], what is Var(X)?
#180. For data set [34, 25, 35, 27, 22], what is the arithmetic mean?
#181. If X~Binomial(n=6, p=0.5), find P(X=5).
#182. Given P(A)=0.3, P(B)=0.2, and P(A∩B)=0.036, find P(A|B).
#183. A discrete random variable has P(X=4)=0.1, P(X=1)=0.3, P(X=1)=0.3, P(X=5)=0.3. Compute E[X].
#184. If T is exponential with rate λ=0.2, find P(T ≤ 1).
#185. A process has population standard deviation 5. For sample size n=17, what is the standard error of the sample mean?
#186. For X~N(μ=71, σ=15), find the z-score of x=56.
#187. If X is uniformly distributed on [12, 19], what is Var(X)?
#188. For data set [38, 13, 17, 29, 20], what is the arithmetic mean?
#189. If X~Binomial(n=8, p=0.5), find P(X=3).
#190. Given P(A)=0.5, P(B)=0.3, and P(A∩B)=0.09, find P(A|B).
#191. A discrete random variable has P(X=4)=0.333, P(X=2)=0.25, P(X=4)=0.083, P(X=2)=0.333. Compute E[X].
#192. If T is exponential with rate λ=0.2, find P(T ≤ 3).
#193. A process has population standard deviation 7. For sample size n=33, what is the standard error of the sample mean?
#194. For X~N(μ=72, σ=8), find the z-score of x=80.
#195. Given P(A)=0.45, P(B|A)=0.7, and P(B|A^c)=0.4, compute P(A|B).
#196. If X is uniformly distributed on [7, 18], what is Var(X)?
#197. For data set [25, 38, 11, 30, 22], what is the arithmetic mean?
#198. If X~Binomial(n=6, p=0.5), find P(X=3).
#199. For standard normal Z, estimate P(Z ≤ 1.5).
#200. Given P(A)=0.6, P(B)=0.3, and P(A∩B)=0.108, find P(A|B).
#201. A discrete random variable has P(X=3)=0.273, P(X=3)=0.273, P(X=5)=0.182, P(X=2)=0.273. Compute E[X].
