急! More about Dispersion 1條

圖片參考：http://faculty.virginia.edu/PullenLab/WJIIIDRBModule/standard%20normal%20distribution.jpg

在於你現在的情況，請留意 mean = 44, s.d.=2。

(a)
Less than 40 = 44-2*2 means Less than mean-2*s.d.
According to the normal bell shape curve and by its symmetric property, the required percentage is (1-95%)/2 = 2.5%

(b)
By part (a), the proportion of boxes having at least 40 pins is 97.5%.
Therefore, 97.5% of the required number of boxes is 3900.
The required number of boxes is 3900/97.5% = 4000.

(c)
Now the question required that 40 is still the number equal to mean-2*s.d.
(The reason is that for a normal distribution (no matter what mean and what s.d.), there must be about 2.5% of data which are less than mean-2*s.d.)
40 = mean - 2*1
mean = 42