Question

Using the accompanying table of​ data, blood platelet counts of women have a​ bell-shaped distribution with a mean of

255.1

and a standard deviation of

65.6

​(All units are 1000

​cells/muμ​L.)

Using​ Chebyshev's theorem, what is known about the percentage of women with platelet counts that are within

33

standard

deviations of the​ mean. What are the minimum and maximum possible platelet counts that are within

3 standard deviations of the​ mean?

..

Click the icon to view the table of platelet counts.

Using​ Chebyshev's theorem, what is known about the percentage of women with platelet counts that are within

3

standard deviations of the​ mean? At least ---- ​% of women have platelet counts within

3 standard deviations of the mean.

317317	225225	256256
297297	374374	260260
285285	235235	230230
264264	228228	389389
216216	308308	239239
249249	310310	235235
385385	228228	232232
219219	373373	271271
506506	187187	263263
351351	243243	248248
328328	289289	273273
190190	228228	279279
243243	178178	331331
251251	261261	245245
185185	327327	329329
394394	185185	297297
195195	184184	202202
232232	293293	197197
229229	228228	175175
215215	290290	333333
222222	239239	209209
170170	216216	228228
337337	264264	261261
241241	207207	257257
274274	184184	280280
254254	245245	234234
577577	308308	222222
158158	252252	258258
187187	234234	221221
248248	208208	183183
397397	265265	324324
216216	224224	261261
238238	213213	211211
197197	254254	231231
201201	170170	250250
204204	356356	207207
226226	166166	239239
219219	321321	254254
182182	171171	305305
252252	296296	274274
316316	269269	393393
213213	165165	180180
242242	167167	308308
172172	378378	230230
314314	218218	189189
342342	284284	237237
245245	340340	133133
212212	244244	245245
239239	224224	293293

Answer 1

Given that, mean = 255.1 and standard deviation = 65.6

According to Chebyshev's theorem, at least (1 - 1/k^{​​​​​​2}​​​) * 100% of the data fall within k standard deviations of the mean.

For k = 3

(1 - 1/3²) * 100 = 0.8889 * 100 = 88.89%

mean - 3sd = 255.1 - (3 * 65.6) = 58.3 and

mean + 3sd = 255.1 + (3 * 65.6) = 451.9

Therefore, minimum and maximum possible platelet counts that are within 3 standard deviations of the mean are :

minimum = 58.3 and maximum = 451.9

At least 88.89% of women have platelet counts within

3 standard deviations of the mean.