Question

A juice machine is set to dispense 16 ounces of juice. The amount of juicedispensed is normally distributed, with a mean of 16.15 ounces and astandard deviation of 0.25 ounces. In which range will the amount of juicedispensed be found 95% of the time?

Answer 1

The empirical rule tells us that 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ) of the mean.

Given,

Mean = 16.15

Standard Deviation = 0.25

Since we are concerned with 95% of data, we are concerned with 2 standard deviations of the mean. That is:

2 x 0.25 = 0.5

Thus, 95% of the values will fall between:

16.15 - 0.5 = 15.65, and

16.15 + 0.5 = 16.65

Looking at the answer choices, the correct answer is B

B. 15.65 ounces to 16.65 ounces