Discuss the below:
Q1 - Consider the NBA Data Set Given:
A. What proportion of these players are less than 74 inches tall?
B. Suppose a random sample of 25 of these players is taken and x is the number of players in the sample who are less than 74 inches tall. Find P(x=0), P(x=1), P(x=2), P(x=3), P(x=4), P(x=5).
C. Note that x in part b has a binomial distribution with λ=np. Use the Poisson probabilities table to approximate P(x=0), P(x=1), P(x=2), P(x=3), P(x=4), P(x=5).
D. Are the probability distributions of parts b and c consistent or is the Poisson approximation inaccurate. Explain.
Q2 - Consider the Data on Heights of NBA Players in the Data Set Given:
A. Use Excel to obtain a histogram. Do these heights appear to be symmetrically distributed? If not, which direction do they seem to be skewed?
B. Compute μ and σ.
C. What percentage of these heights lie in the interval μ - σ to μ +σ ? What about in the interval μ - 2σ to μ + 2σ? In the interval μ - 3σ to μ + 3σ?
D. How do the percentages in part c compare to the corresponding percentages for a normal distribution (68%, 95%, and 99.7% respectively)?
Q3 - Consider the Data on Heights of NBA Players in the Data Set Given:
A. Note μ and σ from previous problem.
B. Take 20 random samples of five players each and find x-bar for each sample.
C. Compute the mean and standard deviation for the set of 20 sample means.
D. Find μ x-bar and σ x-bar for n=5.
E. How do your values of μx-bar and σ x-bar in part d compare with those in part c?
F. What percentage of the 20 sample means found in part b lie in the interval μ x-bar - σ x-bar to μ x-bar + σ x-bar? In the interval μ x-bar - 2σ x-bar to μx-bar + 2σ x-bar? In the interval μx-bar - 3σ x-bar to μx-bar + 3σ x-bar?
G. How do the percentages in part f compare to the corresponding percentages for a normal distribution (68%, 95%, and 99.7% respectively)?
H. Repeat parts b through g using 20 samples of 10 players each.
Q4 - Consider the Data on Heights of NBA Players in the Data Set Given:
A. Take a random sample of 15 players and find a 95% confidence interval for μ . Assume the heights of these players are normally distributed.
B. Repeat part a for samples of size 31 and 45 respectively.
C. Compare the widths of your three confidences.
D. Now calculate the mean, μ , of the heights of all players. Do all of your confidence intervals contain this μ ? If not, which ones do not contain μ ?
Name |
Height |
Weight |
1. Abdul-Wahad, Tariq |
78 |
223 |
2. Abdur-Rahim, Shareef |
81 |
230 |
3. Alexander, Cory |
73 |
190 |
4. Allen, Ray |
77 |
205 |
5. Alston, Rafer |
74 |
173 |
6. Amaechi, John |
82 |
270 |
7. Anderson, Derek |
77 |
195 |
8. Anderson, Kenny |
73 |
168 |
9. Anderson, Nick |
78 |
228 |
10. Anderson, Shandon |
78 |
210 |
11. Anstey, Chris |
84 |
249 |
12. Anthony, Greg |
73 |
180 |
13. Armstrong, B.J. |
74 |
185 |
14. Armstrong, Darrell |
73 |
180 |
15. Artest, Ron |
79 |
246 |
16. Atkins, Chucky |
71 |
160 |
17. Augmon, Stacey |
80 |
205 |
18. Austin, Isaac |
82 |
270 |
19. Avent, Anthony |
81 |
240 |
20. Avery, William |
74 |
180 |
21. Bailey, Toby |
77 |
208 |
22. Baker, Vin |
83 |
250 |
23. Barkley, Charles |
78 |
252 |
24. Barros, Dana |
71 |
163 |
25. Barry, Brent |
78 |
195 |
26. Barry, Jon |
77 |
210 |
27. Battie, Tony |
83 |
240 |
28. Bender, Jonathan |
83 |
210 |
29. Benjamin, Benoit |
84 |
265 |
30. Benjamin, Corey |
78 |
200 |
31. Best, Travis |
71 |
182 |
32. Bibby, Mike |
74 |
190 |
33. Billups, Chauncey |
75 |
202 |
34. Blaylock, Mookie |
73 |
185 |
35. Blount, Corie |
82 |
242 |
36. Bogues, Tyrone |
63 |
141 |
37. Booth, Calvin |
83 |
230 |
38. Borrell, Lazaro |
80 |
220 |
39. Bowdler, Cal |
82 |
245 |
40. Bowen, Bruce |
79 |
200 |
41. Bowen, Ryan |
79 |
215 |
42. Bradley, Shawn |
90 |
248 |
43. Bramlett, A.J. |
82 |
230 |
44. Brand, Elton |
80 |
260 |
45. Brandon, Terrell |
71 |
173 |
46. Brown, Chucky |
80 |
215 |
47. Brown, Dee |
74 |
205 |
48. Brown, Gerald |
76 |
210 |
49. Brown, Marcus |
75 |
185 |
50. Brown, P.J |
83 |
240 |
51. Brown, Randy |
74 |
191 |
52. Brunson, Rick |
76 |
195 |
53. Bryant, Kobe |
78 |
210 |
54. Bryant, Mark |
81 |
245 |
55. Buechler, Jud |
78 |
228 |
56. Buford, Rodney |
77 |
195 |
57. Bullard, Matt |
82 |
235 |
58. Burrell, Scott |
79 |
218 |
59. Caffey, Jason |
80 |
256 |
60. Cage, Michael |
81 |
248 |
61. Camby, Marcus |
83 |
220 |
62. Campbell, Elden |
84 |
255 |
63. Carr, Antoine |
81 |
270 |
64. Carter, Anthony |
73 |
190 |
65. Carter, Vince |
79 |
215 |
66. Cassell, Sam |
75 |
185 |
67. Cato, Kelvin |
83 |
255 |
68. Causwell, Duane |
84 |
240 |
69. Ceballos, Cedric |
79 |
220 |
70. Celestand, John |
76 |
178 |
71. Chapman, Rex |
76 |
195 |
72. Cheaney, Calbert |
79 |
215 |
73. Chilcutt, Pete |
82 |
245 |
74. Childs, Chris |
75 |
195 |
75. Christie, Doug |
78 |
205 |
76. Clark, Keon |
83 |
220 |
77. Closs Jr., Keith |
87 |
212 |
78. Coleman, Derrick |
82 |
260 |
79. Coles, Bimbo |
74 |
182 |
80. Conlon, Marty |
83 |
235 |
81. Corbin, Tyrone |
78 |
225 |
82. Crawford, Chris |
81 |
235 |
83. Croshere, Austin |
81 |
235 |
84. Cummings, Terry |
81 |
250 |
85. Cummings, Vonteego |
75 |
190 |
86. Curry, Dell |
77 |
205 |
87. Curry, Michael |
77 |
227 |
88. Dampier, Erick |
83 |
265 |
89. Daniels, Antonio |
76 |
195 |
90. David, Kornel |
81 |
235 |
91. Davis, Antonio |
81 |
230 |
92. Davis, Baron |
74 |
210 |
93. Davis, Dale |
83 |
230 |
94. Davis, Emanual |
77 |
195 |
95. Davis, Hubert |
77 |
183 |
96. Davis, Ricky |
79 |
195 |
97. Day, Todd |
78 |
188 |
98. DeClercq, Andrew |
82 |
230 |
99. Del Negro, Vinny |
76 |
200 |
100. Delk, Tony |
74 |
189 |
101. Dial, Derrick |
77 |
185 |
102. Dickerson, Michael |
77 |
190 |
103. Divac, Vlade |
85 |
260 |
104. Doleac, Michael |
83 |
265 |
105. Douglas, Sherman |
73 |
195 |
106. Drew, Bryce |
75 |
185 |
107. Dudley, Chris |
83 |
240 |
108. Duncan, Tim |
84 |
248 |
109. Eisley, Howard |
74 |
180 |
110. Ekezie, Obinna |
82 |
262 |
111. Elie, Mario |
77 |
210 |
112. Elliott, Sean |
80 |
220 |
113. Ellis, Dale |
79 |
215 |
114. Ellis, LaPhonso |
80 |
240 |
115. Ellison, Pervis |
82 |
242 |
116. Eschmeyer, Evan |
83 |
245 |
117. Ewing, Patrick |
84 |
240 |
118. Farmer, Tony |
81 |
244 |
119. Feick, Jamie |
80 |
255 |
120. Ferry, Danny |
82 |
235 |
121. Finley, Michael |
79 |
215 |
122. Fisher, Derek |
73 |
200 |
123. Fortson, Danny |
79 |
260 |
124. Foster, Greg |
83 |
250 |
125. Foster, Jeff |
83 |
238 |
126. Fox, Rick |
79 |
242 |
127. Foyle, Adonal |
82 |
250 |
128. Francis, Steve |
75 |
194 |
129. Fuller, Todd |
83 |
255 |
130. Funderburke, Lawrence |
81 |
230 |
131. Garnett, Kevin |
83 |
220 |
132. Garrett, Dean |
83 |
250 |
133. Garrity, Pat |
81 |
231 |
134. Gatling, Chris |
82 |
230 |
135. Geiger, Matt |
85 |
245 |
136. George, Devean |
80 |
220 |
137. Gill, Kendall |
77 |
216 |
138. Gilliam, Armen |
81 |
260 |
139. Glover, Dion |
77 |
228 |
140. Grant, Brian |
81 |
254 |
141. Grant, Gary |
75 |
185 |
142. Grant, Horace |
82 |
245 |
143. Grant, Tyrone |
79 |
240 |
144. Green, A. C. |
81 |
225 |
145. Griffin, Adrian |
77 |
215 |
146. Gugiotta, Tom |
82 |
240 |
147. Ham, Darvin |
79 |
220 |
148. Hamilton, Richard |
78 |
185 |
149. Hamilton, Thomas |
86 |
330 |
150. Hammonds, Tom |
81 |
225 |
151. Hardaway, Anfernee |
79 |
215 |
152. Hardaway, Tim |
72 |
195 |
153. Harper, Ron |
78 |
215 |
154. Harpring, Matt |
79 |
225 |
155. Harrington, Al |
81 |
230 |
156. Harrington, Othella |
81 |
235 |
157. Harris, Lucious |
77 |
205 |
158. Harvey, Antonio |
83 |
246 |
159. Hawkins, Hersey |
75 |
200 |
160. Henderson, Alan |
81 |
235 |
161. Henderson, Cedric |
79 |
215 |
162. Hendrix, Bakari |
80 |
230 |
163. Herren, Chris |
74 |
185 |
164. Hill, Grant |
80 |
225 |
165. Hill, Tyrone |
81 |
250 |
166. Hoiberg, Fred |
76 |
203 |
167. Hood, Derek |
80 |
222 |
168. Hornacek, Jeff |
76 |
190 |
169. Horry, Robert |
82 |
220 |
170. Houston, Allan |
78 |
200 |
171. Howard, Juwan |
81 |
240 |
172. Hudson, Troy |
73 |
170 |
173. Hughes, Larry |
77 |
185 |
174. Hughes, Rick |
81 |
235 |
175. Hunter, Lindsey |
74 |
195 |
176. Ilgauskas, Zydrunas |
87 |
268 |
177. Iverson, Allen |
72 |
165 |
178. Jackson, Bobby |
73 |
185 |
179. Jackson, Jaren |
78 |
215 |
180. Jackson, Jermaine |
76 |
210 |
181. Jackson, Jim |
78 |
220 |
182. Jackson, Mark |
75 |
185 |
183. Jackson, Randell |
83 |
215 |
184. Jacobson, Sam |
76 |
219 |
185. James, Tim |
79 |
221 |
186. Jamison, Antawn |
81 |
223 |
187. Jamison, Harold |
80 |
260 |
188. Johnson, Anthony |
75 |
190 |
189. Johnson, Avery |
71 |
180 |
190. Johnson, DeMarco |
80 |
245 |
191. Johnson, Ervin |
83 |
245 |
192. Johnson, Larry |
79 |
263 |
193. Jones, Charles |
75 |
185 |
194. Jones, Damon |
75 |
185 |
195. Jones, Eddie |
78 |
200 |
196. Jones, Jumaine |
80 |
210 |
197. Jones, Popeye |
80 |
250 |
198. Jordan, Reggie |
76 |
195 |
199. Keefe, Adam |
81 |
230 |
200. Kemp, Shawn |
82 |
256 |
201. Kerr, Steve |
75 |
181 |
202. Kersey, Jerome |
79 |
225 |
203. Ketner, Lari |
81 |
285 |
204. Kidd, Jason |
76 |
212 |
205. King, Gerard |
81 |
250 |
206. Kittles, Kerry |
77 |
179 |
207. Kleine, Joe |
84 |
271 |
208. Knight, Brevin |
70 |
173 |
209. Knight, Travis |
84 |
235 |
210. Kukoc, Toni |
83 |
232 |
211. Laettner, Christian |
83 |
245 |
212. LaFrentz, Raef |
83 |
235 |
213. Lang, Andrew |
83 |
270 |
214. Langdon, Trajan |
75 |
195 |
215. Legler, Tim |
76 |
200 |
216. Lenard, Voshon |
76 |
205 |
217. Lewis, Quincy |
79 |
215 |
218. Lewis, Rashard |
82 |
215 |
219. Livingston, Randy |
76 |
209 |
220. Long, Grant |
81 |
248 |
221. Longley, Luc |
86 |
292 |
222. Lopez, Felipe |
78 |
195 |
223. Lue, Tyronn |
72 |
175 |
224. Lynch, George |
80 |
228 |
225. MacCullough, Todd |
84 |
280 |
226. Maggette, Corey |
78 |
220 |
227. Majerle, Dan |
78 |
220 |
228. Malone, Karl |
81 |
256 |
229. Manning, Danny |
82 |
234 |
230. Marbury, Stephon |
74 |
180 |
231. Marion, Shawn |
79 |
215 |
232. Marks, Sean |
82 |
250 |
233. Marshall, Donyell |
81 |
230 |
234. Martin, Darrick |
71 |
170 |
235. Mashburn, Jamal |
80 |
240 |
236. Mason, Anthony |
80 |
250 |
237. Massenburg, Tony |
81 |
250 |
238. Maxwell, Vernon |
76 |
190 |
239. McCarty, Walter |
82 |
230 |
240. McCloud, George |
80 |
225 |
241. McCoy, Jelani |
82 |
237 |
242. McDyess, Antonio |
81 |
220 |
243. McGrady, Tracy |
80 |
210 |
244. McIlvaine, Jim |
85 |
264 |
245. McKey, Derrick |
82 |
225 |
246. McKie, Aaron |
77 |
209 |
247. McLeod, Roshown |
80 |
220 |
248. Mercer, Ron |
79 |
210 |
249. Meyer, Loren |
82 |
260 |
250. Miller, Andre |
74 |
200 |
251. Miller, Brad |
83 |
250 |
252. Miller, Oliver |
81 |
325 |
253. Miller, Reggie |
79 |
185 |
254. Mills, Chris |
78 |
216 |
255. Mills, Terry |
82 |
250 |
256. Minor, Greg |
78 |
230 |
257. Miskiri, Jason |
74 |
175 |
258. Mitchell, Sam |
79 |
215 |
259. Mobley, Cuttino |
76 |
190 |
260. Mohammed, Nazr |
82 |
240 |
261. Montross, Eric |
84 |
270 |
262. Moore, Mikki |
84 |
230 |
263. Morgunov, Nikita |
82 |
225 |
264. Mourning, Alonzo |
82 |
261 |
265. Mullin, Chris |
79 |
215 |
266. Murdock, Eric |
73 |
200 |
267. Muresan, Gheorghe |
91 |
303 |
268. Murray, Lamond |
79 |
236 |
269. Murray, Tracy |
79 |
228 |
270. Mutombo, Dikembe |
86 |
261 |
271. Nash, Steve |
75 |
195 |
272. Nesby, Tyrone |
78 |
225 |
273. Nesterovic, Radoslav |
84 |
248 |
274. Newman, Johnny |
79 |
205 |
275. Nowitzki, Dirk |
83 |
237 |
276. Oakley, Charles |
81 |
245 |
277. Odom, Lamar |
82 |
220 |
278. Olajuwon, Hakeem |
84 |
255 |
279. Olowokandi, Michael |
85 |
265 |
280. O'Neal, Jermaine |
83 |
226 |
281. O'Neal, Shaquille |
85 |
315 |
282. Ostertag, Greg |
86 |
280 |
283. Outlaw, Charles |
80 |
210 |
284. Overton, Doug |
75 |
190 |
285. Owens, Billy |
81 |
225 |
286. Pack, Robert |
74 |
190 |
287. Padgett, Scott |
81 |
240 |
288. Palacio, Milt |
75 |
195 |
289. Parker, Anthony |
78 |
215 |
290. Parks, Cherokee |
83 |
240 |
291. Patterson, Andrae |
81 |
238 |
292. Patterson, Ruben |
78 |
227 |
293. Payton, Gary |
76 |
180 |
294. Peeler, Anthony |
76 |
208 |
295. Perdue, Will |
84 |
240 |
296. Perkins, Sam |
81 |
260 |
297. Perry, Elliot |
72 |
152 |
298. Person, Chuck |
80 |
241 |
299. Person, Wesley |
78 |
195 |
300. Phills, Bobby |
77 |
220 |
301. Piatkowski, Eric |
79 |
215 |
302. Pierce, Paul |
79 |
220 |
303. Pippen, Scottie |
79 |
228 |
304. Pollard, Scot |
83 |
265 |
305. Polynice, Olden |
84 |
250 |
306. Porter, Terry |
75 |
195 |
307. Posey, James |
80 |
215 |
308. Potapenko, Vitaly |
82 |
280 |
309. Price, Brent |
73 |
185 |
310. Profit, Laron |
77 |
204 |
311. Radojevic, Alexsander |
87 |
245 |
312. Ratliff, Theo |
82 |
225 |
313. Recasner, Eldridge |
75 |
190 |
314. Reeves, Bryant |
84 |
292 |
315. Reid, Don |
80 |
250 |
316. Reid, J.R. |
81 |
255 |
317. Rhodes, Rodrick |
78 |
225 |
318. Rice, Glen |
80 |
220 |
319. Richmond, Mitch |
77 |
215 |
320. Rider, Isaiah |
77 |
215 |
321. Roberts, Stanley |
84 |
290 |
322. Robertson, Ryan |
77 |
190 |
323. Robinson, Cliff |
82 |
225 |
324. Robinson, David |
85 |
250 |
325. Robinson, Eddie |
81 |
210 |
326. Robinson, Glenn |
79 |
235 |
327. Roe, Lou |
79 |
220 |
328. Rogers, Carlos |
83 |
220 |
329. Rogers, Rodney |
79 |
255 |
330. Rogers, Roy |
82 |
235 |
331. Rooks, Sean |
82 |
260 |
332. Rose, Jalen |
80 |
210 |
333. Rose, Malik |
79 |
250 |
334. Ruffin, Michael |
80 |
248 |
335. Russell, Bryon |
79 |
225 |
336. Sabonis, Arvydas |
87 |
292 |
337. Salley, John |
83 |
255 |
338. Schayes, Danny |
83 |
260 |
339. Schrempf, Detlef |
82 |
235 |
340. Scott, Dennis |
80 |
229 |
341. Sealy, Malik |
80 |
200 |
342. Shaw, Brian |
78 |
200 |
343. Simpkins, Dickey |
82 |
264 |
344. Skinner, Brian |
82 |
255 |
345. Smith, Joe |
82 |
225 |
346. Smith, Leon |
82 |
235 |
347. Smith, Michael |
80 |
230 |
348. Smith, Steve |
80 |
215 |
349. Smits, Rik |
88 |
265 |
350. Snow, Eric |
75 |
204 |
351. Spencer, Felton |
84 |
265 |
352. Sprewell, Latrell |
77 |
190 |
353. Stack, Ryan |
83 |
215 |
354. Stackhouse, Jerry |
78 |
218 |
355. Starks, John |
77 |
185 |
356. Stepania, Vladimir |
83 |
236 |
357. Stephens, Joe |
79 |
210 |
358. Stewart, Michael |
82 |
230 |
359. Stith, Bryant |
77 |
208 |
360. Stockton, John |
73 |
175 |
361. Stojakovic, Predrag |
81 |
229 |
362. Stoudamire, Damon |
70 |
171 |
363. Strickland, Erick |
75 |
210 |
364. Strickland, Mark |
81 |
220 |
365. Strickland, Rod |
75 |
185 |
366. Strong, Derek |
81 |
240 |
367. Sundov, Bruno |
86 |
220 |
368. Sura, Bob |
77 |
200 |
369. Szczerbiak, Wally |
79 |
243 |
370. Tabak, Zan |
84 |
245 |
371. Taylor, Johnny |
81 |
220 |
372. Taylor, Maurice |
81 |
260 |
373. Terry, Jason |
74 |
172 |
374. Thomas, John |
81 |
265 |
375. Thomas, Kenny |
80 |
260 |
376. Thomas, Kurt |
81 |
230 |
377. Thomas, Tim |
82 |
230 |
378. Thorpe, Otis |
82 |
246 |
379. Traylor, Robert |
80 |
300 |
380. Trent, Gary |
80 |
250 |
381. Turkcan, Mirsad |
81 |
220 |
382. Van Exel, Nick |
73 |
183 |
383. Van Horn, Keith |
82 |
220 |
384. Vaughn, Jacque |
73 |
190 |
385. Vaught, Loy |
81 |
240 |
386. Vinson, Fred |
76 |
190 |
387. Walker, Antoine |
81 |
245 |
388. Walker, Samaki |
81 |
240 |
389. Wallace, Ben |
81 |
240 |
390. Wallace, John |
81 |
225 |
391. Wallace, Rasheed |
83 |
225 |
392. Walters, Rex |
76 |
190 |
393. Ward, Charlie |
74 |
190 |
394. Weatherspoon, Clarence |
79 |
240 |
395. Webber, Chris |
82 |
245 |
396. Wells, Bonzi |
77 |
210 |
397. Wennington, Bill |
84 |
277 |
398. Wesley, David |
72 |
198 |
399. West, Doug |
78 |
220 |
400. West, Mark |
82 |
246 |
401. White, Jahidi |
81 |
290 |
402. Whitney, Chris |
72 |
170 |
403. Williams, Aaron |
81 |
225 |
404. Williams, Alvin |
77 |
185 |
405. Williams, Eric |
80 |
220 |
406. Williams, Jason |
73 |
190 |
407. Williams, Jayson |
82 |
245 |
408. Williams, Jerome |
81 |
206 |
409. Williams, John |
83 |
245 |
410. Williams, Lorenzo |
81 |
230 |
411. Williams, Monty |
80 |
225 |
412. Williams, Scott |
82 |
230 |
413. Williams, Shammond |
73 |
201 |
414. Williams, Walt |
80 |
230 |
415. Williamson, Corliss |
79 |
245 |
416. Willis, Kevin |
84 |
245 |
417. Willoughby, Dedric |
75 |
190 |
418. Wingate, David |
77 |
187 |
419. Workman, Haywoode |
75 |
200 |
420. Wright, Lorenzen |
83 |
240 |
421. Young, Tim |
86 |
250 |