Question

The vending machine in the school cafeteria usually dispenses about 6 ounces of soft drink. Lately, it is not working properly, and the variability of how much soft drink it dispenses has been gettin greater. The amounts are normally distributed with a standard deviation of 0.2 ounces.
1. What percent of the time will you get between 5.6 and 6.4 ounces?
(a) 13.5%
(b) 34%
(c) 50%
(d) 95%

2. What percent of the time will you get between 6 ounces and 6.2 ounces?
(a) 13.5%
(b) 34%
(c) 50%
(d) 95%

Answer 1

#1) D, 95%
#2) B, 34%

Explanation
#1) The mean is 6 and the standard deviation is 0.2.  5.6 is 0.4 away from the mean; 0.4 is 2 standard deviations.  6.4 is 0.4 away from the mean; again, 0.4 is 2 standard deviations.

The empirical rule states that 95% of data will be within 2 standard deviations of the mean, so 95% is our answer.

#2) 6.2 is only 1 standard deviation away from the mean.  However, this is only half of the percentage from the empirical rule, since we are only considering numbers larger than the mean.  The empirical rule states that 68% of data will fall within 1 standard deviation from the mean, so we have
68/2 = 34%.