The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20.5 hours and a standard deviation of 1.5 hours. a) What is the probability that a car can be assembled at this plant in a period of time: i) less than 19.5 hours

0.25239

Step-by-step explanation:

We start by calculating the z-score

Mathematically;

z-score = (x-mean)/SD

Z-score = (19.5-20.5)/1.5

z-score = -0.667

The probability we want to calculate is;

P( x < -0.667)

we can use the standard normal distribution table to get this

That would be;

0.25239

P( x < -0.667) = 0.25239

x -

median = 1.25

range = 12-14.5

interquartile = q12-q14.5

y -

median = 1

range = 15-17

interquartile = q15-q17