Question

What is the fraction of beans that end near the center (bins 40-60 among 0-100) for the ideal Galton board with 100 layers?

Answer 1

Given : ideal Galton board with 100 layers

To find :   fraction of beans that end near the center (bins 40-60 among 0-100)

Solution:

ideal Galton board   follow normal Distribution

100 layers  hence Mean = 50

SD = (50 - 0)/3   = 50/3

Z score = ( Value - Mean)/SD

Z score for  40 = (40 - 50)/(50/3)  = -0.6

Z score for  60 = (60 - 50)/(50/3)  = 0.6

Z score =  - 0.6  =>  0.2743

Z score =   0.6  =>  0.7257

Data between = 0.7257 - 0.2743  = 0.4514

this is 4514/10000

= 2257/5000

or approximate 9/20  fraction of beans  end near the center (bins 40-60 among 0-100)

9/20  fraction of beans

Learn more:

Assume that adults have iq scores that are normally distributed with ...

https://brainly.in/question/11133397

The mean length of mature whiting is 35 cm and the standard ...

https://brainly.in/question/13450142