Question

The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 11.7 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 11.6 fluid ounces.

(b) Find the probability that the drink is between 11.5 and 11.6 fluid ounces.

(c) Find the probability that the drink is more than 12 fluid ounces. Can this be considered an unusual event? Explain your reasoning.

Is a drink containing more than 12 fluid ounces an unusual event?

Answer 1

Solution :

Given that,

mean = = 11.7

standard deviation = = 0.2

a ) P( x < 11.6 )

P ( x -  / ) < ( 11.6 - 11.7 / 0.2)

P ( z < - 0.1 / 0.2 )

P ( z < -0.5 )

Using z table

= 0.3085

Probability = 0.3085

b ) P(11.5 < x < 11.6 )

P ( 11.5 - 11.7 / 0.2) < ( x -  / ) < ( 11.6 - 11.7 / 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)

= 1 - P(x < 12)

= 1 - P ( x -  / ) < (12 - 11.7 / 0.2)

= 1 - P ( z < 0.3 / 0.2 )

= 1 - P ( z < 1.5 )

Using z table

= 1 - 0.9332

= 0.0668

Probability = 0.0668

This be considered an usual event