Question

A worn, poorly set-up machine is observed to produce components whose length X follows a normal distribution with mean 14 centimeters and standard deviation 3 centimeters. Calculate the probability that the length of a component lies between 19 and 21 centimeters.

• Round your answer to four decimal places.

Answer 1

Population mean, µ = 14

Population standard deviation, σ = 3

Probability that the length of a component lies between 19 and 21 centimeters =

= P(19< X <21)

= P( (19-14)/3 < (X-µ)/σ < (21-14)/3 )

= P(1.67< z < 2.33)

= P(z < 2.33) - P(z < 1.67)

Using excel function:

= NORM.S.DIST(2.33,1) - NORM.S.DIST(1.67,1)

= 0.9901 - 0.9525

= 0.0376 (or 0.0380 without rounding off the z value)