Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.1 millimeters (mm) and a standard deviation of 0.9 mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.)
(a) the thickness is less than 3.0 mm
(b) the thickness is more than 7.0 mm
(c) the thickness is between 3.0 mm and 7.0 mm
math help?
2019-09-15 7:45 am
回答 (1)
2019-09-15 7:58 am
Find the z-scores
(3.0 - 5.1) / 0.9 = z[1]
-2.1 / 0.9 = z[1]
-7/3 = z[1]
-2.3333... = z[1]
(7.0 - 5.1) / 0.9 = z[2]
1.9 / 0.9 = z[2]
19/9 = z[2]
2.111111111..... = z[2]
http://www.z-table.com/
z[1] = -2.33333.... => 0.0099
z[2] = 2.1111.... => 0.9826
The probability that it is 3.0mm or less is 0.0099 or 0.99%
The probability that it is 7.0mm or more is 1 - 0.9826 => 0.0174 or 1.74%
The probability that it is between 3.0mm and 7.0mm is 1 - (0.0099 + 0.0174) = 0.9826 - 0.0099 = 0.9727 or 97.27%
(3.0 - 5.1) / 0.9 = z[1]
-2.1 / 0.9 = z[1]
-7/3 = z[1]
-2.3333... = z[1]
(7.0 - 5.1) / 0.9 = z[2]
1.9 / 0.9 = z[2]
19/9 = z[2]
2.111111111..... = z[2]
http://www.z-table.com/
z[1] = -2.33333.... => 0.0099
z[2] = 2.1111.... => 0.9826
The probability that it is 3.0mm or less is 0.0099 or 0.99%
The probability that it is 7.0mm or more is 1 - 0.9826 => 0.0174 or 1.74%
The probability that it is between 3.0mm and 7.0mm is 1 - (0.0099 + 0.0174) = 0.9826 - 0.0099 = 0.9727 or 97.27%
收錄日期: 2021-04-24 07:39:30
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20190914234532AAta5qq