mathematical and trigonometrical functions

2008-07-19 1:17 am

6.The mass of six concrete blocks were measured before used in construction site as below:
No.123456
Mass (kg)20.020.520.020.520.021.0
a)Calculate the mean, mode, median and standard deviation of the measured set of masses;
b)If two blocks are picked up to use at random, one after the other and without replacement, find the probability that: i) the two blocks picked up are of the same value; ii) one of the blocks picked up is a 20.0 kg and the other is a 20.5kg; and iii) none of the blocks picked up is a 20.0 kg.

回答 (1)

魏王將張遼

2008-07-19 1:52 am

✔ 最佳答案

(a) Mean = (20.0 + 20.5 + 20.0 + 20.5 + 20.0 + 21.0)/6 = 20.33 kg
Median = (20.0 + 20.5)/2 = 20.25 kg
Mode = 20.0 kg
Standard deviation = √{[3 x (20.0 - 20.33)2 + 2 x (20.5 - 20.33)2 + (21.0 - 20.33)2]/6}
= 0.373 kg
(b) For selecting 2 blocks randomly from 6, there are 6C2 = 15 possible combinations.
(i) For same value, it can be either 20.0 or 20.5 kg and for no. of possible combinations:
20.0 kg has 3 possibilities (selecting 2 out of 3)
20.5 kg has 1 possibility (selecting 2 out of 2)
So total probability = 4/15
(ii) Total no. of possible combinations = 3 x 2 = 6 since there are 3 blocks of mass 20.0 kg and 2 blocks of mass 20.5 kg.
So probability is 6/15 = 2/5
(iii) P(1st block is not 20.0 kg) = 3/6 = 1/2
P(2nd block is not 20.0 kg) = 2/5
Therefore the required probability is 1/2 x 2/5 = 1/5

參考: My Maths knowledge

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