Question

A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.7 ounces and standard deviation of 0.3 ounce. Examine the figure below and answer the following questions.



a.) Estimate the probability that the machine will overflow and 8-ounce cup. (Round your answer to two decimal places.)



b.) Estimate the probability that the machine will not overflow an 8-ounce cup. (Round your answer to two decimal places.)



c.) The machine has just been loaded with 4200 cups. How many of these do you expect will overflow when served?

Answer 1

Let X be the amount( in ounces) of soft drink dispensed by the machine .

THen X~ N( 7.7 , 0.3)

So,

a) To find :

  

b) P[ MAchine won't overflow an 8 ounce cup]

= 1- P[X>8]

=P[X<8] = 0.84

c) Let p be the probabilty that a 8 ounce cup overflows .

Then p= 0.16  

Note that this probabliity remains for different cups .

If Y be the number of cups that will overflow out of 4200 cups , then

Y~Bin (n=4200 , p= 0.16)

So, E[Y]= np = 672 .

So 672 cups are expected to be overflowed.