Question

The time it takes to assemble a car in a certain factory is normally distributed with a mean of 20 hours and a standard deviation of 2 hours. [Probability = percent] (a) What is the probability that a car can be assembled in less than 19.4 hours? (b) What is the probability that a car can be assembled between 20 and 22 hours? (c) What is the probability that it will take more than 23 hours to assemble a car? (d) What is the 70th percentile of the car assembling time?

Show Excel formula and value

Answer 1

Given , = 20 , = 2

a)

P(X < 19.4) = ?

Using EXCEL,

P(X < x) = NORM.DIST(x , mean , SD , cumulative)

P(X < 19.4) = NORM.DIST ( 19.4 , 20 , 2 , TRUE )

= 0.3821

b)

P(20 < X < 22) = P(X < 22) - P(X < 20)

Using EXCEL

= NORM.DIST ( 19.4 , 22 , 2 , TRUE ) - NORM.DIST ( 19.4 , 20 , 2 , TRUE )

= 0.8413 - 0.5

= 0.3413

c)

P(X > 23) = ?

= 1 - P(X < 23)

= 1 - NORM.DIST ( 19.4 , 23 , 2 , TRUE ) ( Using EXCEL)

= 1 - 0.9332

= 0.0668

d)

70th pecentile = NORM.INV ( Probabiltiy , mean , SD )

= NORM.INV ( 0.70 , 20 , 2 )

= 21.0488