Cans of regular soda have volumes with a mean of 13.41 oz and a standard deviation of 0.12 oz. Is it unusual for a can to contain 13.49 oz of​ soda?

Question

Cans of regular soda have volumes with a mean of 13.41 oz and a standard deviation of 0.12 oz. Is it unusual for a can to contain 13.49 oz of​ soda?

Minimum​ "usual" value= _____ oz

Answer 1

13.49 - 13.41 = 0.08

one standard deviation = 0.12

0.08/0.12 = 2/3 = about 0.67 standard deviations from the mean or <1 sd

more than 2 standard deviations is unusual as it happens only 1-.95 = 5% of the time

It's the usual probability used in hypothesis testing,

Answer 2

compute z-stat:

z = (13.49 - 13.41)/0.12 = 0.67

13.49 ounce can is only 0.67 standard deviations from the mean, so it is not unusual.

minimum unusual value is for z = -2:

-2 = (x - 13.41)/0.12

x = 13.17