Probability Question 6

Question

The probability that a part produced by a certain factory's assembly line will be defective is .047. Find the probabilities that in a run of 45 items, the following results are obtained. 

 

1.exactly 4 defective items

 

2.no more than 2 items 

 

3.at least defective items

 

 

Answer 1

Define nCr = ( n! ) / ( r! ) / [.( n - r ) ! ].

Then P(r) = nCr * ( p^r ) * [ ( 1 - p) ^(n-r) ].

1. P(4) = [ 45 C 4 ] * ( .047 )⁴ * ( 1 - 0.47 )⁴¹

2. P(0) + P(1) + P(2) = [ 45 C 0 ] * ( 1 - 0.47)⁴⁵

+ [ 45 C 1 ] * ( .047 ) * ( 1 - .047 )⁴⁴

+ [ 45 C 2 ] * ( .047 )² * ( 1 - .047 )⁴³

3. At least how many defective items?

Suppose the number is j:

Σ from m = j to n of [ 45 C j ] * ( .047 )m * ( .953 )^n-m

Note that .953 = 1 - .047

ANY questions?