Question

question 7 of 10
a juice machine is set to dispense 16 ounces of juice. the amount of juice
dispensed is normally distributed, with a mean of 16.15 ounces and a
standard deviation of 0.25 ounces. in which range will the amount of juice
dispensed be found 99.7% of the time?
a. 15.90 ounces to 16.40 ounces
b. 15.65 ounces to 16.65 ounces
c. 15.40 ounces to 16.90 ounces
d. 15.15 ounces to 17.15 ounces

Explanation:

Step1: Recall the empirical rule for normal distribution

The empirical rule states that for a normal distribution, approximately 99.7% of the data lies within 3 standard deviations of the mean.

Step2: Calculate the lower and upper bounds

The mean $\mu = 16.15$ ounces and the standard deviation $\sigma=0.25$ ounces.
The lower bound is $\mu - 3\sigma=16.15-3\times0.25=16.15 - 0.75 = 15.40$ ounces.
The upper bound is $\mu + 3\sigma=16.15+3\times0.25=16.15 + 0.75 = 16.90$ ounces.

Answer:

C. 15.40 ounces to 16.90 ounces