Question

The average time to complete a product on an assembly line is approximately normally distributed with an average of 73 minutes and a σ_n-1= 1.6 minutes.

What % of the time will the assembly line complete a product in > 70 minutes?

What percentage of the time will the assembly line complete a product in < 75 minutes?

What. % of the time will a product be completed on this assembly line between 74 and 77 minutes?

Answer 1

Let X denote time to complete product in assembly line.

1. P(X>70) = P(Z>(70-73)/1.6)

= P( Z> -1.875)

= 0.9692

Thus 96.92% of the time assembly line will complete product in >70 minutes.

B) P(X< 75) = P(Z<(75-73)/1.6)

= P(Z< 1.25)

=0.8944

Thus 89.44% of time assembly line will complete product in <75 minutes.

C. P(74<X<77) = P((74-73)/1.6 < Z < (77-73)/1.6)

= ( 0.625< Z < 2.5)

= 0.259

Thus 25.9% of time assembly line will complete product between 74 and 77 minutes.