Question

The amounts a soft drink machine is designed to dispense for each drink are normally​ distributed, with a mean of

11.711.7

fluid ounces and a standard deviation of

0.20.2

fluid ounce. A drink is randomly selected.

​(a) Find the probability that the drink is less than

11.611.6

fluid ounces.

​(b) Find the probability that the drink is between

11.411.4

and

11.611.6

fluid ounces.

​(c) Find the probability that the drink is more than

1212

fluid ounces. Can this be considered an unusual​ event? Explain your reasoning.

Answer 1

Solution:

Given mean μ = 11.7, Standard deviation sd = 0.2
Normal Distribution = Z= X- μ / sd ~ N(0,1)

a) p(x < 11.6) = p(z < (11.6-11.7)/0.2)=p(z < -0.5) = 0.3085

b) p(11.4 < x < 11.6) = p((11.4-11.7)/0.2 < z < (11.6-11.7)/0.2) = p(-1.5 < z < -0.5) = 0.0668-0.3085= 0.2417

c) p(x > 12)=p(z>(12-11.7)/0.2) = p(z > 1.5)= 0.0668

Yes, probability that drink containing more than 12 fluid ounces is grater than 0.05 so event is not unusual