Question

Question (2): [10 marks]: The time required to assemble an electronic component is normally distributed with a mean of 12 minutes and a standard deviation of 1.5 minutes

a) [2 points] Find the probability that a particular assembly takes more than 14.25 minutes.

b) [2 points] Find (x) the 75th percentile of time required to assemble an electronic component.

c) [3 points] The company wants to increase productivity. One strategy they are discussing is to ensure that 75% of their components are assembled in less than 12 minutes, what must the new average time(?) required to assemble be to meet this criteria, if the standard deviation is held at 1.5 minutes?

Answer 1

Let X be time to required to assemble an electric component

then

a)To find  

=P(z > 1.5)

= 0.0668 ( from z table)

Probability that a particular assembly takes more than 14.25 minutes is 0.0668

b) To find x such that

P( X < x ) = 0.75

From z table

P( z < 0.68) = 0.75

c) To find such that

P( X < 12) = 0.75

We know from z table , P( z < 0.68) =0.75

New average time required to assemble = 10.98 minutes