Question

If only 3% of electric light globes manufactured by a company are defective, use an appropriate approximation to determine the probability that in a random sample of 100 globes manufactured by this company at least one globe is defective. State your answer to four decimal places.

Answer 1

P( defective)=0.03

let x be the number of defective globe

X~ bin( n=100, p=0.03)

mean= np= 100* 0.03=3

variance= np(1-p)= 100 *0.03*(1-0.03)=2.91

now since n=100 is quite high so we will use normal aprroximation

X~ normal( 3, 2.91)

P( atleast one globe is defective)

=P( X>=1)

=P( X> 0.5) {using continuity correction)

=P( z> (0.5- 3)/ sqrt(2.91))

=P( Z>-1.46)

=P(Z<1.46)

=0.9279