Question

A vending machine at Ian Anderson’s Bowling Alley automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6 ounces and a standard deviation of 0.2 ounces.

What percent of cups will be between 7.4 ounces and 8.2 ounces?

What percent of 8 ounce cups will overflow (be over 8 ounces)?

Suppose the machine is loaded with 1000 cups. How many of these cups do you expect will over flow when served?

Answer 1

solution

given that

P(7.4 < x <8.2 ) = P[(7.4 -7.6) /0.2 < (x - ) / < (8.2-7.6) /0.2 )]

= P(-1 < Z <3 )

= P(Z < 3) - P(Z <-1 )

Using z table   

=0.9987-0.1587

=0.8400

answer=84%

(B)P(x > 8 ) = 1 - P(x< 8 )

= 1 - P[(x -) / < (8 -7.6) / 0.2]

= 1 - P(z < 2)

Using z table

= 1 - 0.9772

= 0.0228

answer=2.28%