Question

The amounts a soft drink machine is designed to dispense for each drink are normally? distributed, with a mean of 12.4 fluid ounces and a standard deviation of 0.2

fluid ounce. A drink is randomly selected.?(a) Find the probability that the drink is less than 12.3 fluid ounces.?(b) Find the probability that the drink is between 12.2 and 12.3

fluid ounces.?(c) Find the probability that the drink is more than 12.8 fluid ounces. Can this be considered an unusual? event? Explain your reasoning.

?(a) The probability that the drink is less than 12.3 fluid ounces is nothing .

Answer 1

Solution:

Given that,

   = 12.4

= 0.2

a ) p ( x  < 12.3 )

= p ( x -  / ) < ( 12.3 - 12.4 / 0.2)

= p ( z < - 0.1 /0.2 )

= p ( z < - 0.5 )

Using z table

= 0.3085

Probability = 0.3085

b ) p (12.2 < x  < 12.3 )

= p( 12.2 - 12.4 / 0.2 ) ( x -  / ) < ( 12.3 - 12.4 / 0.2)

= p ( - 0.2 / 0.2 < z < - 0.1 /0.2 )

= p ( - 1 < z < - 0.5)

= p (z < - 0.5 ) - p ( z < - .1 )

Using z table

= 0.3085 - 0.1587

= 0.1498

Probability = 0..1498

c ) p ( x > 12.8 )

= 1 - p (x < 12.8 )

= 1 - p ( x -  / ) < ( 12.8 - 12.4 / 0.2)

= 1 - p ( z < 0.4 /0.2 )

= 1 - p ( z < 2)

Using z table

= 1 - 0.9772

= 0.0228

Probability = 0.0228

The probability is less than 0.05 is  these event is unusual?.