Question

Resistances of certain resistors are uniformly distributed on the interval between 95 Ohms and 103 Ohms

Q: Suppose 3 in 10000 resisters have resistance greater than 110 Ohms. Calculate the probability that at least three resisters out of 5000 would have resistance greater than 110 Ohms. Round the number to two decimal place

Answer 1

Let x be the number of  resisters have resistance greater than 110 Ohms.

x follows Poisson distribution with = 3 per 10000 resisters.

Therefore for 5000 resisters = (3*5000/10000 ) = 1.5

Formula for Poisson distribution is given by,

P( x ) =

We are asked to find P( x ≥ 3 )

P( x ≥ 3 ) = 1 - P( x ≤ 2 )

= 1 -

= 1 - [ 0.2231 + 0.3347 + 0.2510 ]

= 1 - 0.8088

= 0.19