Respuesta :
Answer:
The lengths from 32.1cm to 46.5cm covers 99.7% of this distribution.
Step-by-step explanation:
The 68-95-99.7 rule states that, for normally distributed measures:
68% of the values are within 1 standard deviation of the mean.
95% of the values are within 2 standard deviations of the mean.
99.7% of the values are within 3 standard deviations of the mean.
(a) What range of lengths covers almost all, 99.7%, of this distribution?
Those are those values within 3 standard deviations of the mean. So
From A to B, in which
[tex]A = \mu - 3\sigma = 39.3 - 3(2.4) = 32.1[/tex]
[tex]A = \mu + 3\sigma = 39.3 + 3(2.4) = 46.5[/tex]
The lengths from 32.1cm to 46.5cm covers 99.7% of this distribution.
The solution is:
The range of lengths covering 99.7 % in cm is: ( 32.1 ; 46.5 )
For Normal Distribution, The Empirical Rule ( μ ; σ ) establishes:
- 68 % approximately of all vales will be in the interval ( μ ± σ )
- 95 % approximately of all vales will be in the interval ( μ ± 2σ )
- 99.7 % approximately of all vales will be in the interval ( μ ± 3σ )
a) According to that 99.7 % of all values will be in the interval:
(39.3 ± 3×2.4)
That is: ( 39.3 - 7.2 ; 39.3 + 7.2)
or ( 32.1 ; 46.5 )
