Question

question 19 of 25
the amount of water dispensed by a water dispenser is normally distributed, with a mean of 12.10 ounces and a standard deviation of 0.25 ounces. in which range will the amount of water dispensed be found 68% of the time?
a. 11.35 ounces to 12.85 ounces
b. 11.10 ounces to 13.10 ounces
c. 11.60 ounces to 12.60 ounces
d. 11.85 ounces to 12.35 ounces

Explanation:

Step1: Recall the empirical rule for normal distribution

For a normal distribution, about 68% of the data lies within 1 standard deviation of the mean.

Step2: Calculate the lower and upper bounds

The mean \(\mu = 12.10\) ounces and the standard deviation \(\sigma=0.25\) ounces.
The lower bound is \(\mu-\sigma=12.10 - 0.25=11.85\) ounces.
The upper bound is \(\mu+\sigma=12.10 + 0.25=12.35\) ounces.

Answer:

D. 11.85 ounces to 12.35 ounces