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Please help me

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 95% of the time?
A. 11.85 ounces to 12.35 ounces
B. 11.35 ounces to 12.85 ounces
C. 11.60 ounces to 12.60 ounces
D. 11.10 ounces to 13.10 ounces

Please Help Me The Amount Of Water Dispensed By A Water Dispenser Is Normally Distributed With A Mean Of 1210 Ounces And A Standard Deviation Of 025 Ounces In W class=

Sagot :

Answer:

C. 11.60 ounces to 12.60 ounces

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean 12.10, standard deviation 0.25.

In which range will the amount of water dispensed be found 95% of the time?

By the Empirical Rule, within 2 standard deviations of the mean. So

12.10 - 2*0.25 = 12.10 - 0.5 = 11.60

12.10 + 2*0.25 = 12.10 + 0.5 = 12.6

So the correct answer is given by option C.

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